open-thought/reasoning-gym

Fork 0

mirror of https://github.com/open-thought/reasoning-gym.git synced 2026-04-19 12:58:07 +00:00

Andreas Koepf 5d16a2193c import string_insertion, minor whitespace fixes, gallery update

2025-02-14 07:55:38 +01:00

239 KiB

Raw Blame History

Reasoning Gym Dataset Gallery

This gallery shows examples from all available datasets using their default configurations.

Available Datasets

ab
advanced_geometry
aiw
arc_1d
arc_agi
base_conversion
basic_arithmetic
bf
binary_matrix
caesar_cipher
calendar_arithmetic
chain_sum
color_cube_rotation
complex_arithmetic
count_bits
count_primes
countdown
course_schedule
dice
family_relationships
figlet_font
fraction_simplification
game_of_life
gcd
graph_color
group_anagrams
gsm_symbolic
intermediate_integration
isomorphic_strings
knight_swap
largest_island
lcm
leg_counting
letter_counting
letter_jumble
manipulate_matrix
maze
mini_sudoku
n_queens
number_filtering
number_sequence
number_sorting
palindrome
polynomial_equations
polynomial_multiplication
pool_matrix
power_function
prime_factorization
products
propositional_logic
quantum_lock
ransom_note
rearc
rectangle_count
rotate_matrix
rubiks_cube
self_reference
sentence_reordering
simple_equations
simple_geometry
simple_integration
sokoban
spell_backward
spiral_matrix
string_insertion
string_manipulation
string_synthesis
sudoku
syllogism
time_intervals
tower_of_hanoi
tsumego
word_ladder
word_sequence_reversal
word_sorting
zebra_puzzles

Dataset Examples

ab

Generates A::B tasks, as described by @VictorTaelin here

Default configuration:

seed = 42
size = 500
length = 10

Example tasks:

Example 1:
Question: A::B is a system with 4 tokens: `A#`, `#A`, `B#` and `#B`.

An A::B program is a sequence of tokens. Example:

    B# A# #B #A B#

To *compute* a program, we must rewrite neighbor tokens, using the rules:

    A# #A ... becomes ... nothing
    A# #B ... becomes ... #B A#
    B# #A ... becomes ... #A B#
    B# #B ... becomes ... nothing

In other words, whenever two neighbor tokens have their '#' facing each-other,
they must be rewritten according to the corresponding rule. For example, the
first example shown here is computed as:

    B# A# #B #A B# =
    B# #B A# #A B# =
    A# #A B# =
    B#

The steps were:
1. We replaced `A# #B` by `#B A#`.
2. We replaced `B# #B` by nothing.
3. We replaced `A# #A` by nothing.
The final result was just `B#`.

Now, consider the following program:

A# A# #A B# B# B# A# A# #B A#

Return the final state of the program.

Answer: A# B# B# A# A# A#

Example 2:
Question: A::B is a system with 4 tokens: `A#`, `#A`, `B#` and `#B`.

An A::B program is a sequence of tokens. Example:

    B# A# #B #A B#

To *compute* a program, we must rewrite neighbor tokens, using the rules:

    A# #A ... becomes ... nothing
    A# #B ... becomes ... #B A#
    B# #A ... becomes ... #A B#
    B# #B ... becomes ... nothing

In other words, whenever two neighbor tokens have their '#' facing each-other,
they must be rewritten according to the corresponding rule. For example, the
first example shown here is computed as:

    B# A# #B #A B# =
    B# #B A# #A B# =
    A# #A B# =
    B#

The steps were:
1. We replaced `A# #B` by `#B A#`.
2. We replaced `B# #B` by nothing.
3. We replaced `A# #A` by nothing.
The final result was just `B#`.

Now, consider the following program:

A# #A B# #B #A A# #B #B A# #B

Return the final state of the program.

Answer: #A #B #B #B A# A#

Example 3:
Question: A::B is a system with 4 tokens: `A#`, `#A`, `B#` and `#B`.

An A::B program is a sequence of tokens. Example:

    B# A# #B #A B#

To *compute* a program, we must rewrite neighbor tokens, using the rules:

    A# #A ... becomes ... nothing
    A# #B ... becomes ... #B A#
    B# #A ... becomes ... #A B#
    B# #B ... becomes ... nothing

In other words, whenever two neighbor tokens have their '#' facing each-other,
they must be rewritten according to the corresponding rule. For example, the
first example shown here is computed as:

    B# A# #B #A B# =
    B# #B A# #A B# =
    A# #A B# =
    B#

The steps were:
1. We replaced `A# #B` by `#B A#`.
2. We replaced `B# #B` by nothing.
3. We replaced `A# #A` by nothing.
The final result was just `B#`.

Now, consider the following program:

#B A# B# #B B# #A A# B# A# A#

Return the final state of the program.

Answer: #B B# A# B# A# A#

advanced_geometry

A dataset for advanced geometry tasks using coordinate geometry.

Default configuration:

min_coord = -10
max_coord = 10
size = 50
seed = 42
task_types = ['orthocenter', 'incircle_radius', 'angle_measure']

Example tasks:

Example 1:
Question: In triangle ABC with coordinates A=(-7, -10), B=(-2, -3), and C=(-3, -6), find the measure (in degrees) of angle ABC.
Answer: 17.10°
Metadata: {'A': (-7, -10), 'B': (-2, -3), 'C': (-3, -6), 'angle_ABC_degrees': 17.10272896905237}

Example 2:
Question: For triangle with vertices A=(-1, -6), B=(4, 1), and C=(-7, 4), determine the orthocenter (intersection of altitudes).
Answer: (0.304, -1.217)
Metadata: {'A': (-1, -6), 'B': (4, 1), 'C': (-7, 4), 'orthocenter_exact': ('7/23', '-28/23'), 'orthocenter_approx': (0.30434782608695654, -1.2173913043478262)}

Example 3:
Question: Find the incircle radius of triangle ABC whose vertices are A=(6, 7), B=(-7, -5), and C=(2, -3).
Answer: 2.176
Metadata: {'A': (6, 7), 'B': (-7, -5), 'C': (2, -3), 'incircle_radius_exact': 'sqrt(-sqrt(29) + sqrt(85)/2 + sqrt(313)/2)*sqrt(-sqrt(313)/2 + sqrt(85)/2 + sqrt(29))*sqrt(-sqrt(85)/2 + sqrt(29) + sqrt(313)/2)/sqrt(sqrt(85)/2 + sqrt(29) + sqrt(313)/2)', 'incircle_radius_approx': 2.176123777286009}

aiw

A procedural dataset inspired by the "Alice in Wonderland" paper.

The dataset is inspired by the following paper:
   @inproceedings{nezhurina2024alice,
   title={Alice in Wonderland: Simple Tasks Reveal Severe Generalization and
          Basic Reasoning Deficits in State-Of-the-Art Large Language Models},
   author={Marianna Nezhurina and Lucia Cipolina-Kun and Mehdi Cherti and
          Jenia Jitsev},
   booktitle={NeurIPS 2024 Workshop on Scientific Methods for Understanding
              Deep Learning},
   year={2024},
   url={https://openreview.net/forum?id=Mkl7dzjYiW}
   }

Default configuration:

male_names = ['James', 'John', 'Robert', 'Michael', 'William', 'David', 'Richard', 'Joseph', 'Thomas', 'Charles', 'Bob']
female_names = ['Mary', 'Patricia', 'Jennifer', 'Linda', 'Elizabeth', 'Barbara', 'Susan', 'Jessica', 'Sarah', 'Margaret', 'Alice']
task_types = [<TaskType.SIBLINGS: 'siblings'>, <TaskType.FRIENDS: 'friends'>, <TaskType.COLLEAGUES: 'colleagues'>]
seed = 42
size = 10
max_entities = 6

Example tasks:

Example 1:
Question: Patricia has 6 male colleagues and she also has 3 female colleagues. These are all colleagues that Patricia has. All these mentioned persons around Patricia are colleagues of each other. James has 2 male colleagues and 2 female colleagues in total. All these mentioned persons around James are colleagues of each other. The people in the circle around James do not have other colleagues aside - with the only exception of Matilda. She is colleague of James and she is also colleague of Patricia, being part of Patricia's circle. How many female colleagues does Matilda have?
Answer: 4
Metadata: {'task_type': 'colleagues'}

Example 2:
Question: Elizabeth has 4 brothers and she also has 3 sisters. How many sisters does Elizabeth's brother have?
Answer: 4
Metadata: {'task_type': 'siblings'}

Example 3:
Question: Sarah has 6 male friends and she also has 1 female friends. They all are friends with each other and have no other friends aside. How many female friends does Thomas, a male friend of Sarah, have?
Answer: 2
Metadata: {'task_type': 'friends'}

arc_1d

Generates ARC 1D tasks by randomly selecting from available task generators

This dataset is a procedural variant of the 1D-ARC dataset which is described in the paper:
`LLMs and the Abstraction and Reasoning Corpus:  Successes, Failures, and the Importance
of Object-based Representations` (https://arxiv.org/abs/2305.18354)

Ilya Sheprut (optozorax) created rust generators for most of the ARC 1d tasks. For
reasoning-gym rust tasks were machine-converted to python via Sonnet.

Ilya's original rust code can be found here: https://github.com/optozorax/arc_1d/

Default configuration:

min_size = 10
max_size = 30
num_train = 3
seed = 42
size = 500

Example tasks:

Example 1:
Question: Find the common rule that maps an input grid to an output grid, given the examples below.

Example 1:
Input:  0 0 0 2 9 2 3 4 4 0
Output: 2 9 2 3 4 4 0 0 0 0

Example 2:
Input:  0 0 0 0 4 4 2 1 1 0
Output: 0 4 4 2 1 1 0 0 0 0

Example 3:
Input:  0 0 0 7 9 4 9 1 0 0
Output: 7 9 4 9 1 0 0 0 0 0

Below is a test input grid. Predict the corresponding output grid by applying the rule you found. Describe how you derived the rule and your overall reasoning process in detail before you submit your answer. Your final answer must be placed in <output></output> tags and should be just be the text output grid itself.

Input:
0 0 0 0 0 1 5 0 0 0
Answer: 0 0 1 5 0 0 0 0 0 0
Metadata: {'task_name': 'move_3pix_colorful_left', 'size': 10, 'train_examples': [{'input': [0, 0, 0, 2, 9, 2, 3, 4, 4, 0], 'output': [2, 9, 2, 3, 4, 4, 0, 0, 0, 0]}, {'input': [0, 0, 0, 0, 4, 4, 2, 1, 1, 0], 'output': [0, 4, 4, 2, 1, 1, 0, 0, 0, 0]}, {'input': [0, 0, 0, 7, 9, 4, 9, 1, 0, 0], 'output': [7, 9, 4, 9, 1, 0, 0, 0, 0, 0]}], 'test_example': {'input': [0, 0, 0, 0, 0, 1, 5, 0, 0, 0], 'output': [0, 0, 1, 5, 0, 0, 0, 0, 0, 0]}}

Example 2:
Question: Find the common rule that maps an input grid to an output grid, given the examples below.

Example 1:
Input:  0 0 0 0 0 0 0 6 2 8 8 1 0 0 0 0 0 0 0
Output: 0 0 0 0 0 0 0 0 6 2 8 8 1 0 0 0 0 0 0

Example 2:
Input:  0 6 9 7 7 3 1 2 2 7 3 2 3 9 8 3 7 9 0
Output: 0 0 6 9 7 7 3 1 2 2 7 3 2 3 9 8 3 7 9

Example 3:
Input:  0 0 0 0 0 0 0 0 0 3 7 2 1 1 3 1 3 5 0
Output: 0 0 0 0 0 0 0 0 0 0 3 7 2 1 1 3 1 3 5

Below is a test input grid. Predict the corresponding output grid by applying the rule you found. Describe how you derived the rule and your overall reasoning process in detail before you submit your answer. Your final answer must be placed in <output></output> tags and should be just be the text output grid itself.

Input:
0 9 2 1 2 8 6 6 9 8 0 0 0 0 0 0 0 0 0
Answer: 0 0 9 2 1 2 8 6 6 9 8 0 0 0 0 0 0 0 0
Metadata: {'task_name': 'move_1pix_colorful_right', 'size': 19, 'train_examples': [{'input': [0, 0, 0, 0, 0, 0, 0, 6, 2, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0], 'output': [0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 8, 8, 1, 0, 0, 0, 0, 0, 0]}, {'input': [0, 6, 9, 7, 7, 3, 1, 2, 2, 7, 3, 2, 3, 9, 8, 3, 7, 9, 0], 'output': [0, 0, 6, 9, 7, 7, 3, 1, 2, 2, 7, 3, 2, 3, 9, 8, 3, 7, 9]}, {'input': [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 7, 2, 1, 1, 3, 1, 3, 5, 0], 'output': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 7, 2, 1, 1, 3, 1, 3, 5]}], 'test_example': {'input': [0, 9, 2, 1, 2, 8, 6, 6, 9, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'output': [0, 0, 9, 2, 1, 2, 8, 6, 6, 9, 8, 0, 0, 0, 0, 0, 0, 0, 0]}}

Example 3:
Question: Find the common rule that maps an input grid to an output grid, given the examples below.

Example 1:
Input:  0 0 0 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 0 0 0
Output: 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0

Example 2:
Input:  0 0 0 0 0 0 0 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 0 0 0 0 0 0 0 3 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0

Example 3:
Input:  5 5 5 5 5 5 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 5 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Below is a test input grid. Predict the corresponding output grid by applying the rule you found. Describe how you derived the rule and your overall reasoning process in detail before you submit your answer. Your final answer must be placed in <output></output> tags and should be just be the text output grid itself.

Input:
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0
Answer: 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0
Metadata: {'task_name': 'two_points_and_fill_inv', 'size': 26, 'train_examples': [{'input': [0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0], 'output': [0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0]}, {'input': [0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'output': [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]}, {'input': [5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'output': [5, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]}], 'test_example': {'input': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0], 'output': [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]}}

arc_agi

Default configuration:

use_train = True
use_eval = True
board_format_opts = BoardFormattingOptions(alphabet=['0', '1', '2', '3', '4', '5', '6', '7', '8', '9'], col_delimiter=' ', row_delimiter='\n', array_brackets=False)
rotations = ['90', '180', '270']
mirrors = ['horizontal', 'vertical', 'diagonal', 'counterdiagonal']
use_color_permutation = True
seed = 42
size = 500

Example tasks:

Example 1:
Question: Find the common rule that maps an input grid to an output grid, given the examples below.

Example 1:

Input:
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 6 3 6 7 7 7 7 7 7 7 7 7 7
7 6 6 3 7 6 6 6 7 7 6 3 7 7
7 7 7 7 7 6 3 6 7 7 6 6 7 7
7 7 7 7 7 6 6 3 7 7 7 7 7 7
7 7 7 7 7 3 6 6 7 7 7 6 6 6
7 7 7 7 7 7 7 7 7 7 7 6 3 6
7 6 6 3 7 7 7 7 7 7 7 6 6 6
7 3 6 6 7 7 7 7 7 7 7 7 7 7
7 6 6 6 7 7 7 6 6 6 7 7 7 7
7 7 7 7 7 7 7 6 6 6 7 7 7 7
7 7 7 7 7 7 7 3 6 6 7 7 7 7
7 7 7 7 7 7 7 6 6 6 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7
Output:
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 6 3 7 7
7 7 7 7 7 7 7 7 7 7 6 6 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 6 6 6
7 7 7 7 7 7 7 7 7 7 7 6 3 6
7 7 7 7 7 7 7 7 7 7 7 6 6 6
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 6 6 6 7 7 7 7
7 7 7 7 7 7 7 6 6 6 7 7 7 7
7 7 7 7 7 7 7 3 6 6 7 7 7 7
7 7 7 7 7 7 7 6 6 6 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7

Example 2:

Input:
7 7 7 7 7 6 3 6 7 7 7 6 6 7
7 7 7 7 7 6 6 6 7 7 7 6 6 7
6 6 6 6 7 6 6 6 7 7 7 6 6 7
6 3 6 6 7 7 7 7 7 7 7 7 7 7
6 6 6 6 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 6 6 3 6 7
7 7 7 7 7 7 7 7 7 6 3 6 6 7
7 7 7 6 6 6 6 7 7 6 6 6 3 7
7 7 7 6 6 3 6 7 7 7 7 7 7 7
7 7 7 6 3 6 6 7 7 7 7 7 7 7
7 7 7 6 6 6 6 7 7 7 6 3 6 6
7 7 7 7 7 7 7 7 7 7 6 6 6 3
7 7 7 7 7 7 7 7 7 7 6 3 3 6
7 7 7 7 7 7 7 7 7 7 6 6 6 6
Output:
7 7 7 7 7 6 3 6 7 7 7 6 6 7
7 7 7 7 7 6 6 6 7 7 7 6 6 7
6 6 6 6 7 6 6 6 7 7 7 6 6 7
6 3 6 6 7 7 7 7 7 7 7 7 7 7
6 6 6 6 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7

Example 3:

Input:
7 7 7 7 7 6 6 6 6 7 7 3 6 7 7
6 6 6 6 7 3 6 6 3 7 7 6 3 7 7
6 3 6 6 7 6 6 6 6 7 7 7 7 7 7
6 6 6 6 7 6 6 3 6 7 7 6 6 6 6
7 7 7 7 7 7 7 7 7 7 7 6 3 6 6
7 7 7 7 7 7 7 7 7 7 7 6 6 6 6
7 7 6 6 3 6 6 7 7 7 7 7 7 7 7
7 7 6 6 6 3 6 7 7 7 7 7 7 7 7
7 7 6 3 6 6 6 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 6 6 3 7 7 7
7 7 6 6 6 6 7 7 7 6 3 6 7 7 7
7 7 6 6 6 6 7 7 7 6 6 6 7 7 7
7 7 6 6 6 6 7 7 7 3 6 3 7 7 7
Output:
7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
6 6 6 6 7 7 7 7 7 7 7 7 7 7 7
6 3 6 6 7 7 7 7 7 7 7 7 7 7 7
6 6 6 6 7 7 7 7 7 7 7 6 6 6 6
7 7 7 7 7 7 7 7 7 7 7 6 3 6 6
7 7 7 7 7 7 7 7 7 7 7 6 6 6 6
7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 6 6 6 6 7 7 7 7 7 7 7 7 7
7 7 6 6 6 6 7 7 7 7 7 7 7 7 7
7 7 6 6 6 6 7 7 7 7 7 7 7 7 7


Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Your final answer should just be the text output grid itself.

Input:
7 7 7 7 7 7 7 7 6 3 6 6
6 6 6 7 7 7 7 7 6 6 6 6
3 6 6 7 7 7 7 7 6 3 6 3
6 6 6 7 3 6 6 7 7 7 7 7
7 7 7 7 6 6 6 7 7 7 7 7
7 7 7 7 6 6 3 7 7 7 7 7
7 7 7 7 6 6 6 7 6 6 6 6
7 7 7 7 7 7 7 7 6 6 3 6
7 6 6 6 6 6 6 7 6 6 6 6
7 6 6 6 6 3 6 7 6 6 6 6
7 6 3 6 6 6 6 7 7 7 7 7
7 6 6 6 6 6 6 7 6 6 6 7
7 7 7 7 7 7 7 7 6 6 6 7

Answer: 7 7 7 7 7 7 7 7 7 7 7 7
6 6 6 7 7 7 7 7 7 7 7 7
3 6 6 7 7 7 7 7 7 7 7 7
6 6 6 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 6 6 6 6
7 7 7 7 7 7 7 7 6 6 3 6
7 7 7 7 7 7 7 7 6 6 6 6
7 7 7 7 7 7 7 7 6 6 6 6
7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 6 6 6 7
7 7 7 7 7 7 7 7 6 6 6 7
Metadata: {'input': ((7, 7, 7, 7, 7, 7, 7, 7, 6, 3, 6, 6), (6, 6, 6, 7, 7, 7, 7, 7, 6, 6, 6, 6), (3, 6, 6, 7, 7, 7, 7, 7, 6, 3, 6, 3), (6, 6, 6, 7, 3, 6, 6, 7, 7, 7, 7, 7), (7, 7, 7, 7, 6, 6, 6, 7, 7, 7, 7, 7), (7, 7, 7, 7, 6, 6, 3, 7, 7, 7, 7, 7), (7, 7, 7, 7, 6, 6, 6, 7, 6, 6, 6, 6), (7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 3, 6), (7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6), (7, 6, 6, 6, 6, 3, 6, 7, 6, 6, 6, 6), (7, 6, 3, 6, 6, 6, 6, 7, 7, 7, 7, 7), (7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 7), (7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 7)), 'output': ((7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7), (6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7), (3, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7), (6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7), (7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7), (7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7), (7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6), (7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 3, 6), (7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6), (7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6), (7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7), (7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 7), (7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 7)), 'task_id': 'a934301b'}

Example 2:
Question: Find the common rule that maps an input grid to an output grid, given the examples below.

Example 1:

Input:
2 8 8 8 8 8 8 8 8 9
2 8 8 0 8 8 8 8 8 9
2 8 8 8 8 8 8 8 8 9
2 8 8 8 8 8 8 8 8 9
2 8 8 8 8 0 8 8 8 9
2 8 8 8 8 8 8 8 8 9
2 8 8 8 8 8 8 0 8 9
2 8 8 8 8 8 8 8 8 9
2 8 8 8 8 8 8 8 8 9
2 8 8 8 8 8 8 8 8 9
Output:
2 8 8 8 8 8 8 8 8 9
2 8 8 2 8 8 8 8 8 9
2 8 8 8 8 8 8 8 8 9
2 8 8 8 8 8 8 8 8 9
2 8 8 8 8 9 8 8 8 9
2 8 8 8 8 8 8 8 8 9
2 8 8 8 8 8 8 9 8 9
2 8 8 8 8 8 8 8 8 9
2 8 8 8 8 8 8 8 8 9
2 8 8 8 8 8 8 8 8 9

Example 2:

Input:
6 6 6 6 6 6 6 6 6 6
8 8 8 8 8 8 8 8 8 8
8 8 0 8 8 8 8 8 0 8
8 8 8 8 8 8 0 8 8 8
8 8 8 8 8 8 8 8 8 8
8 8 8 8 8 8 8 8 8 8
8 8 8 8 8 0 8 8 8 8
8 0 8 8 8 8 8 8 8 8
8 8 8 8 8 8 8 8 8 8
1 1 1 1 1 1 1 1 1 1
Output:
6 6 6 6 6 6 6 6 6 6
8 8 8 8 8 8 8 8 8 8
8 8 6 8 8 8 8 8 6 8
8 8 8 8 8 8 6 8 8 8
8 8 8 8 8 8 8 8 8 8
8 8 8 8 8 8 8 8 8 8
8 8 8 8 8 1 8 8 8 8
8 1 8 8 8 8 8 8 8 8
8 8 8 8 8 8 8 8 8 8
1 1 1 1 1 1 1 1 1 1

Example 3:

Input:
5 5 5 5 5 5 5 5 5 5
8 8 8 8 8 8 8 8 8 8
8 8 8 8 8 0 8 8 8 8
8 8 0 8 8 8 8 8 0 8
8 8 8 8 8 8 8 8 8 8
8 8 8 8 8 8 8 8 8 8
8 8 8 0 8 8 8 8 0 8
8 8 8 8 8 8 0 8 8 8
8 8 8 8 8 8 8 8 8 8
7 7 7 7 7 7 7 7 7 7
Output:
5 5 5 5 5 5 5 5 5 5
8 8 8 8 8 8 8 8 8 8
8 8 8 8 8 5 8 8 8 8
8 8 5 8 8 8 8 8 5 8
8 8 8 8 8 8 8 8 8 8
8 8 8 8 8 8 8 8 8 8
8 8 8 7 8 8 8 8 7 8
8 8 8 8 8 8 7 8 8 8
8 8 8 8 8 8 8 8 8 8
7 7 7 7 7 7 7 7 7 7


Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Your final answer should just be the text output grid itself.

Input:
6 8 8 8 8 8 8 8 0 4
6 0 8 8 0 8 8 8 8 4
6 8 8 8 8 8 8 8 8 4
6 8 8 8 8 8 0 8 8 4
6 8 8 0 8 8 8 8 8 4
6 8 8 8 8 8 0 8 8 4
6 8 8 8 8 8 8 8 8 4
6 8 8 8 8 0 8 8 8 4
6 8 8 0 8 8 8 0 8 4
6 8 8 8 8 8 8 8 8 4

Answer: 6 8 8 8 8 8 8 8 4 4
6 6 8 8 6 8 8 8 8 4
6 8 8 8 8 8 8 8 8 4
6 8 8 8 8 8 4 8 8 4
6 8 8 6 8 8 8 8 8 4
6 8 8 8 8 8 4 8 8 4
6 8 8 8 8 8 8 8 8 4
6 8 8 8 8 4 8 8 8 4
6 8 8 6 8 8 8 4 8 4
6 8 8 8 8 8 8 8 8 4
Metadata: {'input': ((6, 8, 8, 8, 8, 8, 8, 8, 0, 4), (6, 0, 8, 8, 0, 8, 8, 8, 8, 4), (6, 8, 8, 8, 8, 8, 8, 8, 8, 4), (6, 8, 8, 8, 8, 8, 0, 8, 8, 4), (6, 8, 8, 0, 8, 8, 8, 8, 8, 4), (6, 8, 8, 8, 8, 8, 0, 8, 8, 4), (6, 8, 8, 8, 8, 8, 8, 8, 8, 4), (6, 8, 8, 8, 8, 0, 8, 8, 8, 4), (6, 8, 8, 0, 8, 8, 8, 0, 8, 4), (6, 8, 8, 8, 8, 8, 8, 8, 8, 4)), 'output': ((6, 8, 8, 8, 8, 8, 8, 8, 4, 4), (6, 6, 8, 8, 6, 8, 8, 8, 8, 4), (6, 8, 8, 8, 8, 8, 8, 8, 8, 4), (6, 8, 8, 8, 8, 8, 4, 8, 8, 4), (6, 8, 8, 6, 8, 8, 8, 8, 8, 4), (6, 8, 8, 8, 8, 8, 4, 8, 8, 4), (6, 8, 8, 8, 8, 8, 8, 8, 8, 4), (6, 8, 8, 8, 8, 4, 8, 8, 8, 4), (6, 8, 8, 6, 8, 8, 8, 4, 8, 4), (6, 8, 8, 8, 8, 8, 8, 8, 8, 4)), 'task_id': '2204b7a8'}

Example 3:
Question: Find the common rule that maps an input grid to an output grid, given the examples below.

Example 1:

Input:
5 5 5 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 8 8 8 8 8 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 8 8 8 8 8 5
5 5 8 8 8 8 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 8 8 8 8 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 8 8 8 8 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 8 8 8 8 5 5 5 5 5
5 5 8 8 8 8 5 5 5 5 5 8 8 8 8 5 5 5 5 5
2 5 8 8 8 8 5 5 5 5 5 8 8 8 8 5 5 5 5 2
5 5 8 8 8 8 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 8 8 8 8 8 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 8 8 8 8 8 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 8 8 8 8 8 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 8 8 8 8 8 5 5 5 8 8 8 8 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 8 8 8 8 5 5
5 5 5 5 5 5 5 2 5 5 5 5 5 5 8 8 8 8 5 5
Output:
5 5 5 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 2 5 5 5 5 5 5 8 8 8 8 8 5
5 5 5 5 5 5 5 2 5 5 5 5 5 5 8 8 8 8 8 5
5 5 8 8 8 8 5 2 5 5 5 5 5 5 5 5 5 5 5 5
5 5 8 8 8 8 5 2 5 5 5 5 5 5 5 5 5 5 5 5
5 5 8 8 8 8 5 2 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 2 5 5 5 2 2 2 2 5 5 5 5 5
5 5 2 2 2 2 5 2 5 5 5 2 2 2 2 5 5 5 5 5
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
5 5 2 2 2 2 5 2 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 2 2 2 2 2 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 2 2 2 2 2 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 2 2 2 2 2 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 2 2 2 2 2 5 5 5 8 8 8 8 5 5
5 5 5 5 5 5 5 2 5 5 5 5 5 5 8 8 8 8 5 5
5 5 5 5 5 5 5 2 5 5 5 5 5 5 8 8 8 8 5 5

Example 2:

Input:
5 5 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 8 8 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 8 8 5 5 5 5 5 8 8 8 5 5 5 5 8 8 8 8
5 5 5 5 5 5 5 5 5 8 8 8 5 5 5 5 8 8 8 8
5 5 5 8 8 8 8 8 5 8 8 8 5 5 5 5 8 8 8 8
5 5 5 8 8 8 8 8 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 8 8 8 8 8 5 5 5 5 5 5 8 8 8 8 5 5
5 5 5 8 8 8 8 8 5 5 5 5 5 5 8 8 8 8 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5 5 5 5
Output:
5 5 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 8 8 5 5 2 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 8 8 5 5 2 5 5 8 8 8 5 5 5 5 8 8 8 8
5 5 5 5 5 5 2 5 5 8 8 8 5 5 5 5 8 8 8 8
5 5 5 2 2 2 2 2 5 8 8 8 5 5 5 5 8 8 8 8
5 5 5 2 2 2 2 2 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 2 2 2 2 2 5 5 5 5 5 5 8 8 8 8 5 5
5 5 5 2 2 2 2 2 5 5 5 5 5 5 8 8 8 8 5 5
5 5 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5 5 5 5

Example 3:

Input:
5 8 8 8 8 8 5 2 5 5 5 5 5 5
5 8 8 8 8 8 5 5 5 5 5 8 8 8
5 5 5 5 5 5 5 5 5 5 5 8 8 8
5 5 5 5 8 8 8 8 8 8 5 8 8 8
5 5 5 5 8 8 8 8 8 8 5 8 8 8
5 5 5 5 8 8 8 8 8 8 5 8 8 8
8 8 5 5 8 8 8 8 8 8 5 5 5 5
8 8 5 5 8 8 8 8 8 8 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 8 8 8 5 5 8 8 8 5 5 5 5
2 5 8 8 8 5 5 8 8 8 5 5 5 2
5 5 8 8 8 5 5 5 5 5 5 5 5 5
5 5 8 8 8 5 5 2 5 5 5 5 5 5
Output:
5 8 8 8 8 8 5 2 5 5 5 5 5 5
5 8 8 8 8 8 5 2 5 5 5 8 8 8
5 5 5 5 5 5 5 2 5 5 5 8 8 8
5 5 5 5 2 2 2 2 2 2 5 8 8 8
5 5 5 5 2 2 2 2 2 2 5 8 8 8
5 5 5 5 2 2 2 2 2 2 5 8 8 8
8 8 5 5 2 2 2 2 2 2 5 5 5 5
8 8 5 5 2 2 2 2 2 2 5 5 5 5
5 5 5 5 5 5 5 2 5 5 5 5 5 5
5 5 2 2 2 5 5 2 2 2 5 5 5 5
2 2 2 2 2 2 2 2 2 2 2 2 2 2
5 5 2 2 2 5 5 2 5 5 5 5 5 5
5 5 2 2 2 5 5 2 5 5 5 5 5 5


Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Your final answer should just be the text output grid itself.

Input:
5 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 8 8 8 8 8 8 8 8 8 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 8 8 8 8 8 8 8 8 8 5 5 5 8 8 5 5 5 5 5 5
5 5 5 5 5 8 8 8 8 8 8 8 8 8 5 5 5 8 8 5 5 8 8 8 5
5 5 5 5 5 8 8 8 8 8 8 8 8 8 5 5 5 5 5 5 5 8 8 8 5
5 5 5 5 5 8 8 8 8 8 8 8 8 8 5 5 5 5 5 5 5 8 8 8 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 8 8 8 8 8 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 8 8 8 8 8 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
2 8 8 8 8 8 5 5 5 8 8 5 5 5 5 5 5 5 5 5 5 5 5 5 2
5 8 8 8 8 8 5 5 5 8 8 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 8 8 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 8 8 5
5 5 5 5 5 5 5 5 5 5 5 5 5 8 8 8 8 8 5 5 5 5 8 8 5
5 5 5 5 5 5 5 5 5 5 5 5 5 8 8 8 8 8 5 5 5 5 8 8 5
5 5 5 5 8 8 8 5 5 5 5 5 5 8 8 8 8 8 5 5 5 5 5 5 5
2 5 5 5 8 8 8 5 5 5 5 5 5 8 8 8 8 8 5 8 8 8 8 5 2
5 5 5 5 8 8 8 5 5 8 8 8 5 8 8 8 8 8 5 8 8 8 8 5 5
5 5 5 5 5 5 5 5 5 8 8 8 5 5 5 5 5 5 5 8 8 8 8 5 5
5 5 5 5 5 5 5 5 5 8 8 8 5 5 5 5 5 5 5 8 8 8 8 5 5
5 5 5 5 5 2 5 5 5 8 8 8 5 5 5 5 5 5 5 5 5 5 5 5 5

Answer: 5 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 2 2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 2 2 2 2 2 2 2 2 2 5 5 5 8 8 5 5 5 5 5 5
5 5 5 5 5 2 2 2 2 2 2 2 2 2 5 5 5 8 8 5 5 8 8 8 5
5 5 5 5 5 2 2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 8 8 8 5
5 5 5 5 5 2 2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 8 8 8 5
5 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 2 2 2 2 2 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 2 2 2 2 2 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
5 2 2 2 2 2 5 5 5 2 2 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 2 5 5 5 2 2 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 8 8 5
5 5 5 5 5 2 5 5 5 5 5 5 5 2 2 2 2 2 5 5 5 5 8 8 5
5 5 5 5 5 2 5 5 5 5 5 5 5 2 2 2 2 2 5 5 5 5 8 8 5
5 5 5 5 2 2 2 5 5 5 5 5 5 2 2 2 2 2 5 5 5 5 5 5 5
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
5 5 5 5 2 2 2 5 5 2 2 2 5 2 2 2 2 2 5 2 2 2 2 5 5
5 5 5 5 5 2 5 5 5 2 2 2 5 5 5 5 5 5 5 2 2 2 2 5 5
5 5 5 5 5 2 5 5 5 2 2 2 5 5 5 5 5 5 5 2 2 2 2 5 5
5 5 5 5 5 2 5 5 5 2 2 2 5 5 5 5 5 5 5 5 5 5 5 5 5
Metadata: {'input': ((5, 5, 5, 5, 5, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), (5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), (5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), (5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5), (5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 8, 8, 5, 5, 8, 8, 8, 5), (5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 8, 8, 8, 5), (5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 8, 8, 8, 5), (5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), (5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), (5, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), (5, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), (2, 8, 8, 8, 8, 8, 5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2), (5, 8, 8, 8, 8, 8, 5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), (5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), (5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5), (5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 5, 5, 5, 5, 8, 8, 5), (5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 5, 5, 5, 5, 8, 8, 5), (5, 5, 5, 5, 8, 8, 8, 5, 5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5), (2, 5, 5, 5, 8, 8, 8, 5, 5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 5, 8, 8, 8, 8, 5, 2), (5, 5, 5, 5, 8, 8, 8, 5, 5, 8, 8, 8, 5, 8, 8, 8, 8, 8, 5, 8, 8, 8, 8, 5, 5), (5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 8, 8, 8, 8, 5, 5), (5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 8, 8, 8, 8, 5, 5), (5, 5, 5, 5, 5, 2, 5, 5, 5, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5)), 'output': ((5, 5, 5, 5, 5, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), (5, 5, 5, 5, 5, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), (5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), (5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5), (5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 8, 8, 5, 5, 8, 8, 8, 5), (5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 8, 8, 8, 5), (5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 8, 8, 8, 5), (5, 5, 5, 5, 5, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), (5, 5, 5, 5, 5, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), (5, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), (5, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2), (5, 2, 2, 2, 2, 2, 5, 5, 5, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), (5, 5, 5, 5, 5, 2, 5, 5, 5, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), (5, 5, 5, 5, 5, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5), (5, 5, 5, 5, 5, 2, 5, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 5, 5, 5, 5, 8, 8, 5), (5, 5, 5, 5, 5, 2, 5, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 5, 5, 5, 5, 8, 8, 5), (5, 5, 5, 5, 2, 2, 2, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5), (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2), (5, 5, 5, 5, 2, 2, 2, 5, 5, 2, 2, 2, 5, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 5, 5), (5, 5, 5, 5, 5, 2, 5, 5, 5, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 5, 5), (5, 5, 5, 5, 5, 2, 5, 5, 5, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 5, 5), (5, 5, 5, 5, 5, 2, 5, 5, 5, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5)), 'task_id': '0d87d2a6'}

base_conversion

Generates base conversion tasks

Default configuration:

min_base = 2
max_base = 16
min_value = 0
max_value = 1000
seed = 42
size = 500

Example tasks:

Example 1:
Question: Convert the base-3 number 220020 to binary
Answer: 1010001110
Metadata: {'decimal_value': 654, 'source_base': 3, 'target_base': 2, 'source_repr': '220020', 'target_repr': '1010001110'}

Example 2:
Question: Convert the base-6 number 103 to base-13 (use lowercase letters a-z for digits above 9)
Answer: 30
Metadata: {'decimal_value': 39, 'source_base': 6, 'target_base': 13, 'source_repr': '103', 'target_repr': '30'}

Example 3:
Question: Convert the base-10 number 418 to base-13 (use lowercase letters a-z for digits above 9)
Answer: 262
Metadata: {'decimal_value': 418, 'source_base': 10, 'target_base': 13, 'source_repr': '418', 'target_repr': '262'}

basic_arithmetic

Dataset that generates basic arithmetic tasks with configurable complexity

Default configuration:

min_terms = 2
max_terms = 6
min_digits = 1
max_digits = 4
operators = ('+', '-', '*', '/')
allow_parentheses = True
allow_negation = True
seed = 42
size = 500
format_style = simple
whitespace = single

Example tasks:

Example 1:
Question: -5 * -6 =
Answer: 30
Metadata: {'num_terms': 2, 'num_digits': 1, 'expression': '-5 * -6'}

Example 2:
Question: 965 / 5 =
Answer: 193
Metadata: {'num_terms': 2, 'num_digits': 3, 'expression': '965 / 5'}

Example 3:
Question: 0 + -2 + -4 * 0 * 3 =
Answer: -2
Metadata: {'num_terms': 5, 'num_digits': 1, 'expression': '0 + -2 + -4 * 0 * 3'}

bf

Generates BF tasks

Default configuration:

seed = 42
size = 500
difficulty = 1

Example tasks:

Example 1:
Question: This is a BF (Brainf*ck) computer program. What is the output? 

>[-]>[-]<>++++++++++[<+++++++++++>-]<+.-.+++++.--------------.+++++++++++++++.<
Answer: onset
Metadata: {'bfit_code': '\nint main() {\n    print("onset");\n}\n', 'bf_program': '>[-]>[-]<>++++++++++[<+++++++++++>-]<+.-.+++++.--------------.+++++++++++++++.<'}

Example 2:
Question: This is a BF (Brainf*ck) computer program. What is the output? 

>[-]>[-]<>++++++++[<++++++++++++++>-]<.-----------.+++++++++++++.---------------.+++++.<
Answer: perch
Metadata: {'bfit_code': '\nint main() {\n    print("perch");\n}\n', 'bf_program': '>[-]>[-]<>++++++++[<++++++++++++++>-]<.-----------.+++++++++++++.---------------.+++++.<'}

Example 3:
Question: This is a BF (Brainf*ck) computer program. What is the output? 

>[-]>[-]<>+++++++++[<+++++++++++++>-]<.-------.----------.+.+++++++++++++.<
Answer: under
Metadata: {'bfit_code': '\nint main() {\n    print("under");\n}\n', 'bf_program': '>[-]>[-]<>+++++++++[<+++++++++++++>-]<.-------.----------.+.+++++++++++++.<'}

binary_matrix

Generates Binary Matrix exercises with configurable difficulty

Default configuration:

max_n = 10
p_zero = 0.25
size = 500
seed = 42

Example tasks:

Example 1:
Question: Given a square matrix, your job is to find the taxicab distance of the nearest 0 for each cell.

Example:

Input: Find the distance to the nearest 0 for each cell in the matrix below:
0 0 0
0 1 0
1 1 1

Output:
0 0 0
0 1 0
1 2 1

Find the distance to the nearest 0 for each cell in the matrix below:
0 0
1 0

Answer: 0 0
1 0
Metadata: {'matrix': [[0, 0], [1, 0]], 'solution': [[0, 0], [1, 0]]}

Example 2:
Question: Given a square matrix, your job is to find the taxicab distance of the nearest 0 for each cell.

Example:

Input: Find the distance to the nearest 0 for each cell in the matrix below:
0 0 0
0 1 0
1 1 1

Output:
0 0 0
0 1 0
1 2 1

Find the distance to the nearest 0 for each cell in the matrix below:
0

Answer: 0
Metadata: {'matrix': [[0]], 'solution': [[0]]}

Example 3:
Question: Given a square matrix, your job is to find the taxicab distance of the nearest 0 for each cell.

Example:

Input: Find the distance to the nearest 0 for each cell in the matrix below:
0 0 0
0 1 0
1 1 1

Output:
0 0 0
0 1 0
1 2 1

Find the distance to the nearest 0 for each cell in the matrix below:
1 0 1 1 0 1 1
1 0 1 1 1 1 1
1 1 1 1 0 1 1
1 1 1 1 0 0 1
0 1 1 1 1 1 0
1 0 1 1 1 1 0
1 1 1 1 1 1 1

Answer: 1 0 1 1 0 1 2
1 0 1 2 1 2 3
2 1 2 1 0 1 2
1 2 2 1 0 0 1
0 1 2 2 1 1 0
1 0 1 2 2 1 0
2 1 2 3 3 2 1
Metadata: {'matrix': [[1, 0, 1, 1, 0, 1, 1], [1, 0, 1, 1, 1, 1, 1], [1, 1, 1, 1, 0, 1, 1], [1, 1, 1, 1, 0, 0, 1], [0, 1, 1, 1, 1, 1, 0], [1, 0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 1, 1, 1]], 'solution': [[1, 0, 1, 1, 0, 1, 2], [1, 0, 1, 2, 1, 2, 3], [2, 1, 2, 1, 0, 1, 2], [1, 2, 2, 1, 0, 0, 1], [0, 1, 2, 2, 1, 1, 0], [1, 0, 1, 2, 2, 1, 0], [2, 1, 2, 3, 3, 2, 1]]}

caesar_cipher

Generates Caesar cipher encryption/decryption tasks

Default configuration:

delimiter = .
min_words = 3
max_words = 20
min_rotation = 1
max_rotation = 25
seed = 42
size = 500

Example tasks:

Example 1:
Question: Decrypt this Caesar cipher text: JNJUBUF ZPVS BTTPDJBUF XIPN J XBT DPNQMJNFOUJOH B NPNFOU BHP
Answer: IMITATE YOUR ASSOCIATE WHOM I WAS COMPLIMENTING A MOMENT AGO
Metadata: {'rotation': 1, 'cipher_text': 'JNJUBUF ZPVS BTTPDJBUF XIPN J XBT DPNQMJNFOUJOH B NPNFOU BHP', 'clear_text': 'IMITATE YOUR ASSOCIATE WHOM I WAS COMPLIMENTING A MOMENT AGO'}

Example 2:
Question: Decrypt this Caesar cipher text: PBSDJ XKZYVOYX CWSDR LYEQRD SD PYB K WOBO KXN YBSQSXKDON DOVOZRYXSM TYEBXKVSCW
Answer: FRITZ NAPOLEON SMITH BOUGHT IT FOR A MERE AND ORIGINATED TELEPHONIC JOURNALISM
Metadata: {'rotation': 10, 'cipher_text': 'PBSDJ XKZYVOYX CWSDR LYEQRD SD PYB K WOBO KXN YBSQSXKDON DOVOZRYXSM TYEBXKVSCW', 'clear_text': 'FRITZ NAPOLEON SMITH BOUGHT IT FOR A MERE AND ORIGINATED TELEPHONIC JOURNALISM'}

Example 3:
Question: Decrypt this Caesar cipher text: ZW PFLI JKFDRTY ZJ FLK FW ZK DLJK SV DVEUVU
Answer: IF YOUR STOMACH IS OUT OF IT MUST BE MENDED
Metadata: {'rotation': 17, 'cipher_text': 'ZW PFLI JKFDRTY ZJ FLK FW ZK DLJK SV DVEUVU', 'clear_text': 'IF YOUR STOMACH IS OUT OF IT MUST BE MENDED'}

calendar_arithmetic

Default configuration:

year = 2022
tasks = ['weekday_offset', 'weekday_of_date', 'weekday_of_date_from_first_day', 'recurring_event_day', 'count_days', 'count_business_days', 'is_leap_year']
offset_upper_bound = 100
leap_year_range = 200
seed = 42
size = 500

Example tasks:

Example 1:
Question: Between Sunday, February 27, 2022 and Wednesday, March 2, 2022 (counting both dates), what's the total count of business days (Monday through Friday)? Give the count numerically.
Answer: 3
Metadata: {'task': 'count_business_days', 'start_date': '2022-02-27', 'end_date': '2022-03-02'}

Example 2:
Question: Starting from Monday, May 23, 2022, which weekday was it 98 days before? Write out the full weekday name.
Answer: Monday
Metadata: {'task': 'weekday_offset', 'start_date': '2022-05-23', 'offset_days': -98, 'target_date': '2022-02-14'}

Example 3:
Question: If a meeting is scheduled on the last Saturday of September 2022, on which day of the month does it occur? Respond with just the number. Answer with -1 if the ordinal does not exist in the month.
Answer: 24
Metadata: {'task': 'recurring_event_day', 'year': 2022, 'month': 9, 'ordinal': 'last', 'weekday': 'Saturday'}

chain_sum

Generates simple arithmetic tasks using only + and - operators

Default configuration:

min_terms = 2
max_terms = 6
min_digits = 1
max_digits = 4
allow_negation = False
seed = 42
size = 500

Example tasks:

Example 1:
Question: 4 + 3 =
Answer: 7
Metadata: {'difficulty': {'num_terms': 2, 'num_digits': 1}, 'expression': '4 + 3'}

Example 2:
Question: 812 + 880 =
Answer: 1692
Metadata: {'difficulty': {'num_terms': 2, 'num_digits': 3}, 'expression': '812 + 880'}

Example 3:
Question: 2 + 6 + 3 + 4 + 0 =
Answer: 15
Metadata: {'difficulty': {'num_terms': 5, 'num_digits': 1}, 'expression': '2 + 6 + 3 + 4 + 0'}

color_cube_rotation

Generates color cube rotation reasoning tasks

Default configuration:

min_rotations = 1
max_rotations = 3
seed = 42
size = 500

Example tasks:

Example 1:
Question: A cube has:
- a pink top side
- a gray right side
- a orange front side
- a purple left side
- a indigo back side
- a cyan bottom side

The cube is rotated so that the side which was before at the bottom is now at the top.

What is now the color of the back side of the cube?
Answer: orange
Metadata: {'initial_state': {'top': 'pink', 'right': 'gray', 'front': 'orange', 'left': 'purple', 'back': 'indigo', 'bottom': 'cyan'}, 'rotations': ['bottom'], 'target_side': 'back', 'num_rotations': 1}

Example 2:
Question: A cube has:
- a gray top side
- a brown right side
- a silver front side
- a red left side
- a purple back side
- a yellow bottom side

The cube is rotated so that the side which was before at the left is now at the top.

Next, the bottom side is rotated to become the top face.

After that the cube is turned to make the bottom face the top.

What is now the color of the left side of the cube?
Answer: yellow
Metadata: {'initial_state': {'top': 'gray', 'right': 'brown', 'front': 'silver', 'left': 'red', 'back': 'purple', 'bottom': 'yellow'}, 'rotations': ['left', 'bottom', 'bottom'], 'target_side': 'left', 'num_rotations': 3}

Example 3:
Question: A cube has:
- a orange top side
- a cyan right side
- a violet front side
- a pink left side
- a gray back side
- a gold bottom side

The cube is rotated so that the side which was before at the left is now at the top.

Now the cube is rotated to place its back side at the top.

Now the cube is rotated to place its bottom side at the top.

What is now the color of the left side of the cube?
Answer: gold
Metadata: {'initial_state': {'top': 'orange', 'right': 'cyan', 'front': 'violet', 'left': 'pink', 'back': 'gray', 'bottom': 'gold'}, 'rotations': ['left', 'back', 'bottom'], 'target_side': 'left', 'num_rotations': 3}

complex_arithmetic

Generates complex number arithmetic problems.

Default configuration:

min_real = -10
max_real = 10
min_imag = -10
max_imag = 10
operations = ('+', '-', '*', '/')
seed = 42
size = 500

Example tasks:

Example 1:
Question: Add the complex numbers: (-10.0 - 2.0i) + (-3.0 - 3.0i)
Answer: -13.0 - 5.0i
Metadata: {'num1': (-10.0, -2.0), 'num2': (-3.0, -3.0), 'operation': '+', 'result': (-13, -5)}

Example 2:
Question: Add the complex numbers: (-1.0 - 6.0i) + (4.0 + 1.0i)
Answer: 3.0 - 5.0i
Metadata: {'num1': (-1.0, -6.0), 'num2': (4.0, 1.0), 'operation': '+', 'result': (3, -5)}

Example 3:
Question: Divide the complex numbers: (-7.0 - 79.0i) ÷ (-7.0 - 5.0i)
Answer: 6.0 + 7.0i
Metadata: {'num1': (-7.0, -79.0), 'num2': (-7.0, -5.0), 'operation': '/', 'result': (6, 7)}

count_bits

Generates Count Bits exercises with configurable difficulty

Default configuration:

max_n = 2147483647
size = 500
seed = 42

Example tasks:

Example 1:
Question: How many 1 bits are there in the binary representation of the number 1373158607?
Answer: 18
Metadata: {'number': 1373158607, 'solution': 18, 'binary': '1010001110110001011110011001111'}

Example 2:
Question: How many 1 bits are there in the binary representation of the number 82789451?
Answer: 14
Metadata: {'number': 82789451, 'solution': 14, 'binary': '100111011110100010001001011'}

Example 3:
Question: How many 1 bits are there in the binary representation of the number 877324117?
Answer: 16
Metadata: {'number': 877324117, 'solution': 16, 'binary': '110100010010101110011101010101'}

count_primes

Generates Count Primes exercises with configurable difficulty

Default configuration:

max_n = 10000
size = 500
seed = 42

Example tasks:

Example 1:
Question: Count how many prime numbers there are between 1825 and 2029 (inclusive) ?
Answer: 27
Metadata: {'start': 1825, 'end': 2029, 'primes': [False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, True], 'solution': 27}

Example 2:
Question: Count how many prime numbers there are between 632 and 5319 (inclusive) ?
Answer: 589
Metadata: {'start': 632, 'end': 5319, 'primes': [False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False], 'solution': 589}

Example 3:
Question: Count how many prime numbers there are between 6694 and 8824 (inclusive) ?
Answer: 236
Metadata: {'start': 6694, 'end': 8824, 'primes': [False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, True, False, True, False, False, False], 'solution': 236}

countdown

Generates Countdown Number Game tasks

Default configuration:

min_numbers = 4
max_numbers = 6
min_value = 1
max_value = 100
min_target = 100
max_target = 999
operators = ('+', '-', '*', '/')
shuffle = True
seed = 42
size = 500

Example tasks:

Example 1:
Question: Calculate 139 using the numbers 36, 29, 95, 32, 4, 15.
Each number may be used at most once.
Answer: 15 - 4 + 95 + 36 - 32 + 29
Metadata: {'numbers': [36, 29, 95, 32, 4, 15], 'target': 139, 'expression': '15 - 4 + 95 + 36 - 32 + 29'}

Example 2:
Question: Using the numbers 74, 48, 56, 66, create an expression that equals 132.
You can only use each number once.
Answer: 66 - 56 + 74 + 48
Metadata: {'numbers': [74, 48, 56, 66], 'target': 132, 'expression': '66 - 56 + 74 + 48'}

Example 3:
Question: Using the numbers 5, 41, 38, 81, 14, create an expression that equals 450.
You can only use each number once.
Answer: 41*14 - 81 - 38 - 5
Metadata: {'numbers': [5, 41, 38, 81, 14], 'target': 450, 'expression': '41*14 - 81 - 38 - 5'}

course_schedule

Generates Course Schedule exercises with configurable difficulty

Default configuration:

num_courses = 5
max_num_prerequisites = 2
p_solvable = 0.5
min_cycle_length = 3
max_cycle_length = 5
size = 500
seed = 42

Example tasks:

Example 1:
Question: There are a total of 5 courses you have to take, labeled from 0 to 4.

You are given the following list of prerequisites, where prerequisites[i] = (a_i, b_i) indicates that you must first take course b_i if you want to take course a_i:
[(2, 1), (4, 2), (4, 3), (2, 3)]

Return True if you can finish all courses considering the prerequisites, or False otherwise.

Answer: True
Metadata: {'courses': [3, 1, 2, 4, 0], 'prerequisites': [(2, 1), (4, 2), (4, 3), (2, 3)], 'solution': True, 'solvable': True}

Example 2:
Question: There are a total of 5 courses you have to take, labeled from 0 to 4.

You are given the following list of prerequisites, where prerequisites[i] = (a_i, b_i) indicates that you must first take course b_i if you want to take course a_i:
[(3, 0), (2, 4), (2, 3), (4, 1), (3, 1), (0, 1), (0, 2), (1, 3)]

Return True if you can finish all courses considering the prerequisites, or False otherwise.

Answer: False
Metadata: {'courses': [1, 4, 3, 2, 0], 'prerequisites': [(3, 0), (2, 4), (2, 3), (4, 1), (3, 1), (0, 1), (0, 2), (1, 3)], 'solution': False, 'solvable': False}

Example 3:
Question: There are a total of 5 courses you have to take, labeled from 0 to 4.

You are given the following list of prerequisites, where prerequisites[i] = (a_i, b_i) indicates that you must first take course b_i if you want to take course a_i:
[]

Return True if you can finish all courses considering the prerequisites, or False otherwise.

Answer: True
Metadata: {'courses': [2, 1, 4, 0, 3], 'prerequisites': [], 'solution': True, 'solvable': True}

dice

Generates Dice-based puzzles with configurable parameters

Default configuration:

num_dice = 4
max_dice_size = 20
seed = 42
size = 500

Example tasks:

Example 1:
Question: I have these dice: 1d20, 1d10, 1d5, 1d2. What are the odds of rolling 18 or higher? (Assume that all dice are rolled at once, and that '1d6' represents one roll of a 6-sided dice.) Please respond with a reduced fraction representing the probability [ex., 1/60].
Answer: 13/20

Example 2:
Question: I have these dice: 1d20, 1d11, 1d6, 1d3. What are the odds of rolling 23 or higher? (Assume that all dice are rolled at once, and that '1d6' represents one roll of a 6-sided dice.) Please respond with a reduced fraction representing the probability [ex., 1/60].
Answer: 19/40

Example 3:
Question: I have these dice: 1d20, 1d19, 1d18, 1d15. What are the odds of rolling 48 or higher? (Assume that all dice are rolled at once, and that '1d6' represents one roll of a 6-sided dice.) Please respond with a reduced fraction representing the probability [ex., 1/60].
Answer: 9677/51300

family_relationships

Generates family relationship reasoning tasks

Default configuration:

min_family_size = 4
max_family_size = 8
male_names = ['James', 'John', 'Robert', 'Michael', 'William', 'David', 'Richard', 'Joseph', 'Thomas', 'Charles', 'Peter', 'Daniel', 'Matthew', 'Christopher', 'Andrew', 'George', 'Edward', 'Benjamin', 'Henry', 'Samuel', 'Alexander', 'Oliver', 'Jack', 'Harry', 'Jacob', 'Noah', 'Ethan', 'Lucas', 'Mason', 'Logan', 'Sebastian', 'Theodore', 'Owen', 'Liam', 'Aiden', 'Kai', 'Jayden', 'Zion', 'Phoenix', 'Atlas', 'Axel', 'Ryder', 'Finn']
female_names = ['Mary', 'Patricia', 'Jennifer', 'Linda', 'Elizabeth', 'Barbara', 'Susan', 'Jessica', 'Sarah', 'Karen', 'Emma', 'Lisa', 'Anna', 'Margaret', 'Victoria', 'Charlotte', 'Sophia', 'Isabella', 'Olivia', 'Ava', 'Mia', 'Emily', 'Abigail', 'Amelia', 'Eleanor', 'Grace', 'Alice', 'Lucy', 'Chloe', 'Sophie', 'Lily', 'Hannah', 'Zoe', 'Luna', 'Nova', 'Aria', 'Willow', 'Aurora', 'Sage', 'River', 'Winter', 'Sky', 'Rain']
seed = 42
size = 500

Example tasks:

Example 1:
Question: John is married to Isabella. They have a child called Edward. Edward is married to Victoria.

What is Isabella to Edward?
Answer: mother
Metadata: {'person1': 'Isabella', 'person2': 'Edward', 'relationship': 'mother', 'family_size': 4}

Example 2:
Question: Henry is married to Karen. They have a child called Sebastian. Sebastian is married to Eleanor.

What relation is Henry to Karen?
Answer: husband
Metadata: {'person1': 'Henry', 'person2': 'Karen', 'relationship': 'husband', 'family_size': 4}

Example 3:
Question: Liam is married to Nova. They have a child called Noah. Noah is married to Charlotte. They have a child called Patricia. Joseph is married to Lisa. They have a child called Charlotte.

What is Liam to Noah?
Answer: father
Metadata: {'person1': 'Liam', 'person2': 'Noah', 'relationship': 'father', 'family_size': 7}

figlet_font

Generates FigletFont tasks

Default configuration:

static_word = None
static_font = None
space_letters = True
seed = 42
size = 500

Example tasks:

Example 1:
Question: Please read the following figlet font:

  sSSSs        d s  b        sss.      d sss        sss sssss 
 S     S       S  S S      d           S                S     
S       S      S   SS      Y           S                S     
S       S      S    S        ss.       S sSSs           S     
S       S      S    S           b      S                S     
 S     S       S    S           P      S                S     
  "sss"        P    P      ` ss'       P sSSss          P     
                                                              

Answer: ONSET
Metadata: {'font': 'amc_tubes', 'space_letters': True}

Example 2:
Question: What word does this say?

######   ######   ######     ####   ##    ## 
 ##  ##   ##  ##   ##  ##   ##  ##   ##  ##  
 ##  ##   ##       ##  ##  ##   ##   ##  ##  
 #####    ####     #####   ##        ######  
 ##       ##       ## ##   ##   ##   ##  ##  
 ##       ##  ##   ## ##    ##  ##   ##  ##  
####     ######   ### ###    ####   ##    ## 
                                             

Answer: PERCH
Metadata: {'font': 'demo_2__', 'space_letters': True}

Example 3:
Question: What word does this say?

                                              
                                              
                                              
### ###   ### ###   #####    ######   #####   
 ## ##     ##  #     ## ##    ##  #    ## ##  
 ## ##     ### #     ## ##    ####     ## ##  
 ## ##     #####     ## ##    ##       ####   
 ## ##     ## ##     ## ##    ## ##    ## ##  
  ###     ### ##    #####    ######   #### ## 
                                              
                                              

Answer: UNDER
Metadata: {'font': 'xcourb', 'space_letters': True}

fraction_simplification

Generates fraction simplification tasks

Default configuration:

min_value = 1
max_value = 1000
min_factor = 1
max_factor = 100
styles = ('plain', 'latex_inline', 'latex_frac', 'latex_dfrac')
seed = 42
size = 500

Example tasks:

Example 1:
Question: Simplify the fraction $\frac{92}{524}$ to its lowest terms
Answer: $\frac{23}{131}$
Metadata: {'numerator': 92, 'denominator': 524, 'simplified_numerator': 23, 'simplified_denominator': 131, 'reduction_factor': 4, 'style': 'latex_frac'}

Example 2:
Question: Simplify the fraction $3600/26370$ to its lowest terms
Answer: $40/293$
Metadata: {'numerator': 3600, 'denominator': 26370, 'simplified_numerator': 40, 'simplified_denominator': 293, 'reduction_factor': 90, 'style': 'latex_inline'}

Example 3:
Question: Simplify the fraction 29330/37310 to its lowest terms
Answer: 419/533
Metadata: {'numerator': 29330, 'denominator': 37310, 'simplified_numerator': 419, 'simplified_denominator': 533, 'reduction_factor': 70, 'style': 'plain'}

game_of_life

Generates Game of Life games with configurable parameters

Default configuration:

grid_size_x = 10
grid_size_y = 10
filled_cells = 100
simulation_steps = 1
seed = 42
size = 500

Example tasks:

Example 1:
Question: What will this Game of Life board look like after 1 steps of simulation? Reply as array of array representing rows in the grid from top to bottom in JSON format. (An empty 3x3 grid would look like this: [[0,0,0],[0,0,0],[0,0,0]])

[[0,1,0,1,1,0,0,0,1,0],
 [1,0,0,1,0,1,1,1,1,1],
 [0,0,1,1,1,1,1,1,1,0],
 [1,1,1,1,0,0,0,0,1,1],
 [1,1,1,1,0,0,1,0,1,1],
 [1,1,0,1,1,0,1,1,0,1],
 [1,0,0,1,1,0,0,0,0,1],
 [1,1,1,0,0,1,1,0,1,1],
 [1,1,1,1,1,0,0,1,0,1],
 [0,1,1,1,0,1,1,0,1,0]].
Answer: [[0,1,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0,0,0],[0,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0,1,0]]
Metadata: {'grid_size_x': 10, 'grid_size_y': 10, 'filled_cells': 100, 'simulation_steps': 1}

Example 2:
Question: What will this Game of Life board look like after 1 steps of simulation? Reply as array of array representing rows in the grid from top to bottom in JSON format. (An empty 3x3 grid would look like this: [[0,0,0],[0,0,0],[0,0,0]])

[[1,1,1,1,1,1,0,1,1,1],
 [0,0,1,1,1,1,1,1,1,1],
 [0,1,0,0,0,0,0,1,1,1],
 [1,0,0,1,1,1,1,0,0,1],
 [0,1,0,1,1,0,0,1,1,0],
 [1,1,1,1,0,1,1,0,1,1],
 [0,1,1,0,1,1,1,0,0,1],
 [0,0,1,0,1,1,0,0,1,1],
 [0,1,1,0,1,0,1,0,1,1],
 [1,1,1,0,1,1,1,0,0,1]].
Answer: [[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,1,0,1,0,1,1,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0]]
Metadata: {'grid_size_x': 10, 'grid_size_y': 10, 'filled_cells': 100, 'simulation_steps': 1}

Example 3:
Question: What will this Game of Life board look like after 1 steps of simulation? Reply as array of array representing rows in the grid from top to bottom in JSON format. (An empty 3x3 grid would look like this: [[0,0,0],[0,0,0],[0,0,0]])

[[0,1,0,1,1,1,1,0,0,1],
 [0,1,0,0,1,1,1,0,1,1],
 [0,1,1,1,1,0,1,0,1,0],
 [1,0,0,1,1,0,1,1,1,1],
 [1,1,1,0,0,1,1,0,1,1],
 [0,1,0,0,1,1,0,1,0,1],
 [0,1,1,0,0,0,1,0,1,1],
 [0,1,1,0,1,1,1,1,0,1],
 [1,1,1,1,1,1,0,1,1,0],
 [1,1,1,0,0,1,1,0,1,0]].
Answer: [[0,0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,1,1],[0,1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1,0]]
Metadata: {'grid_size_x': 10, 'grid_size_y': 10, 'filled_cells': 100, 'simulation_steps': 1}

gcd

Generates Greatest Common Divisor (GCD) tasks

Default configuration:

min_numbers = 2
max_numbers = 2
min_value = 1
max_value = 1000
seed = 42
size = 500

Example tasks:

Example 1:
Question: Find the Greatest Common Divisor (GCD) of these numbers: 26, 760
Answer: 2
Metadata: {'numbers': [26, 760], 'result': 2}

Example 2:
Question: Find the Greatest Common Divisor (GCD) of these numbers: 688, 716
Answer: 4
Metadata: {'numbers': [688, 716], 'result': 4}

Example 3:
Question: Find the Greatest Common Divisor (GCD) of these numbers: 297, 30
Answer: 3
Metadata: {'numbers': [297, 30], 'result': 3}

graph_color

Generates graph coloring problems with configurable parameters

Default configuration:

num_colors = 4
num_vertices = 10
edge_probability = 0.4
seed = 42
size = 500

Example tasks:

Example 1:
Question: Please provide a coloring for this graph such that every vertex is not connected to a vertex of the same color. The graph has these properties:

Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [(0, 2), (0, 3), (0, 4), (0, 8), (1, 2), (1, 3), (1, 5), (1, 6), (1, 9), (2, 5), (2, 8), (2, 9), (3, 5), (3, 6), (3, 7), (4, 9), (6, 9), (7, 8), (7, 9), (8, 9)]
Possible colors: [1, 2, 3, 4]

Return your solution as a JSON map of verteces to colors. (For example: {0: 1, 1: 2, 2: 3})

Answer: None
Metadata: {'possible_answer': {0: 1, 1: 1, 2: 2, 3: 2, 4: 2, 5: 3, 6: 3, 7: 1, 8: 3, 9: 4}, 'puzzle': {'vertices': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'edges': [(0, 2), (0, 3), (0, 4), (0, 8), (1, 2), (1, 3), (1, 5), (1, 6), (1, 9), (2, 5), (2, 8), (2, 9), (3, 5), (3, 6), (3, 7), (4, 9), (6, 9), (7, 8), (7, 9), (8, 9)], 'num_colors': 4, 'color_options': [1, 2, 3, 4]}}

Example 2:
Question: Please provide a coloring for this graph such that every vertex is not connected to a vertex of the same color. The graph has these properties:

Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [(0, 1), (0, 3), (0, 9), (1, 3), (1, 8), (2, 4), (2, 5), (3, 6), (3, 7), (3, 8), (4, 6), (4, 9), (6, 7), (7, 9)]
Possible colors: [1, 2, 3, 4]

Return your solution as a JSON map of verteces to colors. (For example: {0: 1, 1: 2, 2: 3})

Answer: None
Metadata: {'possible_answer': {0: 1, 1: 2, 2: 1, 3: 3, 4: 2, 5: 2, 6: 1, 7: 2, 8: 1, 9: 3}, 'puzzle': {'vertices': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'edges': [(0, 1), (0, 3), (0, 9), (1, 3), (1, 8), (2, 4), (2, 5), (3, 6), (3, 7), (3, 8), (4, 6), (4, 9), (6, 7), (7, 9)], 'num_colors': 4, 'color_options': [1, 2, 3, 4]}}

Example 3:
Question: Please provide a coloring for this graph such that every vertex is not connected to a vertex of the same color. The graph has these properties:

Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [(0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 5), (1, 8), (1, 9), (2, 5), (2, 6), (2, 7), (2, 9), (3, 6), (3, 7), (4, 5), (4, 6), (4, 7), (4, 8), (5, 8), (6, 9)]
Possible colors: [1, 2, 3, 4]

Return your solution as a JSON map of verteces to colors. (For example: {0: 1, 1: 2, 2: 3})

Answer: None
Metadata: {'possible_answer': {0: 1, 1: 1, 2: 1, 3: 1, 4: 2, 5: 3, 6: 3, 7: 3, 8: 4, 9: 2}, 'puzzle': {'vertices': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'edges': [(0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 5), (1, 8), (1, 9), (2, 5), (2, 6), (2, 7), (2, 9), (3, 6), (3, 7), (4, 5), (4, 6), (4, 7), (4, 8), (5, 8), (6, 9)], 'num_colors': 4, 'color_options': [1, 2, 3, 4]}}

group_anagrams

Generates Group Anagrams exercises with configurable difficulty

Default configuration:

anagram_groups = 10
max_words_per_group = 5
size = 500
seed = 42

Example tasks:

Example 1:
Question: An anagram is a word formed by rearranging the letters of a different word, using all the original letters exactly once.

Your job is to group the anagrams together. You can return the answer in any order.

Example:
Input: ["eat", "tea", "tan", "ate", "nat", "bat"]
Output: [["bat"], ["nat", "tan"], ["ate", "eat", "tea"]]
Explanation:
    - There is no string in the input that can be rearranged to form "bat".
    - The strings "nat" and "tan" are anagrams as they can be rearranged to form each other.

Group the following list of words into anagrams:
["tinglers", "argonon", "ditas", "palinodist", "merocyte", "conterminal", "canny", "nancy", "outasight", "autosight", "oversauciness", "applauders", "suprapedal"]

Answer: [["applauders", "suprapedal"], ["argonon"], ["autosight", "outasight"], ["canny", "nancy"], ["conterminal"], ["ditas"], ["merocyte"], ["oversauciness"], ["palinodist"], ["tinglers"]]
Metadata: {'words': ['tinglers', 'argonon', 'ditas', 'palinodist', 'merocyte', 'conterminal', 'canny', 'nancy', 'outasight', 'autosight', 'oversauciness', 'applauders', 'suprapedal'], 'solution': [['applauders', 'suprapedal'], ['argonon'], ['autosight', 'outasight'], ['canny', 'nancy'], ['conterminal'], ['ditas'], ['merocyte'], ['oversauciness'], ['palinodist'], ['tinglers']]}

Example 2:
Question: An anagram is a word formed by rearranging the letters of a different word, using all the original letters exactly once.

Your job is to group the anagrams together. You can return the answer in any order.

Example:
Input: ["eat", "tea", "tan", "ate", "nat", "bat"]
Output: [["bat"], ["nat", "tan"], ["ate", "eat", "tea"]]
Explanation:
    - There is no string in the input that can be rearranged to form "bat".
    - The strings "nat" and "tan" are anagrams as they can be rearranged to form each other.

Group the following list of words into anagrams:
["regear", "escrod", "coders", "decors", "credos", "scored", "semitaur", "muriates", "peripterous", "zanies", "expatiater", "wooled", "meningomyelocele", "myelomeningocele", "vainest", "natives", "naivest", "preludes", "repulsed"]

Answer: [["coders", "credos", "decors", "escrod", "scored"], ["expatiater"], ["meningomyelocele", "myelomeningocele"], ["muriates", "semitaur"], ["naivest", "natives", "vainest"], ["peripterous"], ["preludes", "repulsed"], ["regear"], ["wooled"], ["zanies"]]
Metadata: {'words': ['regear', 'escrod', 'coders', 'decors', 'credos', 'scored', 'semitaur', 'muriates', 'peripterous', 'zanies', 'expatiater', 'wooled', 'meningomyelocele', 'myelomeningocele', 'vainest', 'natives', 'naivest', 'preludes', 'repulsed'], 'solution': [['coders', 'credos', 'decors', 'escrod', 'scored'], ['expatiater'], ['meningomyelocele', 'myelomeningocele'], ['muriates', 'semitaur'], ['naivest', 'natives', 'vainest'], ['peripterous'], ['preludes', 'repulsed'], ['regear'], ['wooled'], ['zanies']]}

Example 3:
Question: An anagram is a word formed by rearranging the letters of a different word, using all the original letters exactly once.

Your job is to group the anagrams together. You can return the answer in any order.

Example:
Input: ["eat", "tea", "tan", "ate", "nat", "bat"]
Output: [["bat"], ["nat", "tan"], ["ate", "eat", "tea"]]
Explanation:
    - There is no string in the input that can be rearranged to form "bat".
    - The strings "nat" and "tan" are anagrams as they can be rearranged to form each other.

Group the following list of words into anagrams:
["eagerest", "granitite", "helium", "nizam", "nazim", "striplings", "slipstring", "rearrest", "arrester", "bf", "tadpolism", "canun", "cunan", "isotonic"]

Answer: [["arrester", "rearrest"], ["bf"], ["canun", "cunan"], ["eagerest"], ["granitite"], ["helium"], ["isotonic"], ["nazim", "nizam"], ["slipstring", "striplings"], ["tadpolism"]]
Metadata: {'words': ['eagerest', 'granitite', 'helium', 'nizam', 'nazim', 'striplings', 'slipstring', 'rearrest', 'arrester', 'bf', 'tadpolism', 'canun', 'cunan', 'isotonic'], 'solution': [['arrester', 'rearrest'], ['bf'], ['canun', 'cunan'], ['eagerest'], ['granitite'], ['helium'], ['isotonic'], ['nazim', 'nizam'], ['slipstring', 'striplings'], ['tadpolism']]}

gsm_symbolic

Default configuration:

difficulty = 1.0
seed = 42
size = 500

Example tasks:

Example 1:
Question: There are 12 students playing basketball and twice that number playing volleyball. There are 17 boys and 17 girls playing table tennis. If each student only participates in one group, how many students are there in total?
Answer: 70
Metadata: {'difficulty': 1.0, 'answer_value': 70, 'answer_cot': 'There are 12 x 2 = 24 students playing volleyball.\nThere are 17 + 17 = 34 students playing table tennis.\nIn total there are 12 + 24 + 34 = 70 students.\n#### 70', 'variables': {'tennis_players': 12, 'volleyball_players': 24, 'soccer_boys': 17, 'soccer_girls': 17, 'total_soccer': 34, 'total_students': 70, 'sports': ['basketball', 'volleyball', 'table tennis']}}

Example 2:
Question: In Ms. Johnson's class of 100 students, 80% of the class are volleyball players. Out of the remaining class, 65% of the students are choir members or part of robotics club members. These 3 groups of students will need to leave early today to travel to an away performance. How many students are leaving early?
Answer: 93
Metadata: {'difficulty': 1.0, 'answer_value': 93, 'answer_cot': "80% of the 100 student class are volleyball players so that's 0.8*100 = 80 students\nThere are 100 students and 80 are volleyball players so that leaves 100-80 = 20 students\n65% of the remaining 20 students are part of robotics club members or choir members so that's 0.65*20 = 13 students\n80 students are volleyball players and 13 are part of robotics club members/choir members so 80+13 = 93 students will be leaving early\n#### 93", 'variables': {'teacher': 'Ms. Johnson', 'total_students': 100, 'percent_group1': 80, 'percent_group23': 65, 'group1': 'volleyball players', 'group2': 'choir members', 'group3': 'robotics club members', 'event': 'performance', 'group1_count': 80, 'group23_count': 13}}

Example 3:
Question: Olivia is trying to decide whether to do her business accounting herself or hire an accountant. If she does it herself, she'll be able to do 7 fewer hours of consulting work, losing €57/hour in missed income. The accountant charges €57. How much more money will she have if she hires the accountant?
Answer: 342
Metadata: {'difficulty': 1.0, 'answer_value': 342, 'answer_cot': "First find the total lost revenue if Olivia does her business accounting herself: €57/hour * 7 hours = €399\nThen subtract the accountant's charge to find how much money Olivia saves: €399 - €57 = €342\n#### 342", 'variables': {'name': 'Olivia', 'task': 'her business accounting', 'profession': 'accountant', 'hours': 7, 'work_type': 'consulting', 'hourly_rate': 57, 'fee': 57, 'currency': '€', 'lost_income': 399}}

intermediate_integration

Generates intermediate integration problem - either by substitution or by parts

Default configuration:

problem_types = ('substitution', 'by_parts')
substitution_types = ('linear', 'trigonometric', 'exponential', 'radical')
by_parts_types = ('polynomial_exp_trig', 'log_inverse_trig', 'cyclic', 'repeated_parts')
seed = 42
size = 500
linear_lower_bound = 1
linear_upper_bound = 10
min_linear_degree = 2
max_linear_degree = 4
outer_constant_min = 1
outer_constant_max = 3
min_poly_degree = 1
max_poly_degree = 3
symbols = ('x', 'X')
operators = ('+', '-')

Example tasks:

Example 1:
Question: Find the indefinite integral: ∫ -3*exp(3*x + 9) dx
In addition, when doing calculation, use the following instructions together with your mathematical ingenuity to solve the integral problems
## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
## 2. Always use * when doing all sorts of multiplcation in your reasoning steps. For example Use [-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C] instead of [-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C].

Answer: -exp(3*x + 9) + C
Metadata: {'integrand': '-3*exp(3*x + 9)', 'problem_type': 'substitution', 'variable': 'x', 'type': 'exponential', 'expected_answer_expression': -exp(3*x + 9)}

Example 2:
Question: Evaluate the indefinite integral: ∫ -6*sin(2*X + 10)*cos(2*X + 10)**4 dx
In addition, when doing calculation, use the following instructions together with your mathematical ingenuity to solve the integral problems
## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
## 2. Always use * when doing all sorts of multiplcation in your reasoning steps. For example Use [-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C] instead of [-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C].

Answer: 3*cos(2*X + 10)**5/5 + C
Metadata: {'integrand': '-6*sin(2*X + 10)*cos(2*X + 10)**4', 'problem_type': 'substitution', 'variable': 'X', 'type': 'trigonometric', 'expected_answer_expression': 3*cos(2*X + 10)**5/5}

Example 3:
Question: Find the indefinite integral: ∫ 2*asin(x) dx
In addition, when doing calculation, use the following instructions together with your mathematical ingenuity to solve the integral problems
## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
## 2. Always use * when doing all sorts of multiplcation in your reasoning steps. For example Use [-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C] instead of [-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C].

Answer: 2*Integral(asin(x), x) + C
Metadata: {'integrand': '2*asin(x)', 'problem_type': 'by_parts', 'variable': 'x', 'type': 'log_inverse_trig', 'expected_answer_expression': 2*Integral(asin(x), x)}

isomorphic_strings

Generates Isomorphic Strings exercises with configurable difficulty

Default configuration:

max_string_length = 10
p_solvable = 0.5
size = 500
seed = 42

Example tasks:

Example 1:
Question: Two strings are isomorphic if the characters in one string can be replaced to get the second string.

All occurrences of a character must be replaced with another character while preserving the order of characters.

No two characters may map to the same character, but a character may map to itself.

Example 1:
Input: egg add
Output: True
Explanation: The strings s and t can be made identical by:
    - Mapping 'e' to 'a'.
    - Mapping 'g' to 'd'.

Example 2:
Input: foo bar
Output: False
Explanation:
    - The strings cannot be made identical as 'o' needs to be mapped to both 'a' and 'r'.

Return True if the following two strings are isomorphic, or False otherwise:
cc bw

Answer: False
Metadata: {'words': ['cc', 'bw'], 'solution': False, 'solvable': False}

Example 2:
Question: Two strings are isomorphic if the characters in one string can be replaced to get the second string.

All occurrences of a character must be replaced with another character while preserving the order of characters.

No two characters may map to the same character, but a character may map to itself.

Example 1:
Input: egg add
Output: True
Explanation: The strings s and t can be made identical by:
    - Mapping 'e' to 'a'.
    - Mapping 'g' to 'd'.

Example 2:
Input: foo bar
Output: False
Explanation:
    - The strings cannot be made identical as 'o' needs to be mapped to both 'a' and 'r'.

Return True if the following two strings are isomorphic, or False otherwise:
nai oik

Answer: True
Metadata: {'words': ['nai', 'oik'], 'solution': True, 'solvable': True}

Example 3:
Question: Two strings are isomorphic if the characters in one string can be replaced to get the second string.

All occurrences of a character must be replaced with another character while preserving the order of characters.

No two characters may map to the same character, but a character may map to itself.

Example 1:
Input: egg add
Output: True
Explanation: The strings s and t can be made identical by:
    - Mapping 'e' to 'a'.
    - Mapping 'g' to 'd'.

Example 2:
Input: foo bar
Output: False
Explanation:
    - The strings cannot be made identical as 'o' needs to be mapped to both 'a' and 'r'.

Return True if the following two strings are isomorphic, or False otherwise:
hogtytyof kgqwfwfgh

Answer: True
Metadata: {'words': ['hogtytyof', 'kgqwfwfgh'], 'solution': True, 'solvable': True}

knight_swap

Generates Knight Swap puzzles with configurable parameters.

Default configuration:

min_nodes = 6
max_nodes = 9
min_pieces = 2
max_pieces = 2
min_steps = 4
max_steps = 20
max_attempts = 100
seed = 42
size = 5
impossible_ratio = 0.2

Example tasks:

Example 1:
Question: Knight Swap Challenge:

```
    A   B   C   D
   ----------------
3 |   | . |   | . |
   ----------------
2 | B | w |   |   |
   ----------------
1 |   |   | B | w |
   ----------------
```

Legend:
- 'w' = White Knight
- 'B' = Black Knight
- Empty squares are marked with '.'

Objective:
Swap the positions of all white knights with all black knights through valid moves.

Rules:
1. Knights move in L-shape (2 squares + 1 square perpendicular)
2. Knights can only move to empty squares
3. w moves first, then players alternate
4. All knights must reach their target positions (white ↔ black)

Question:
Is it possible to swap all knights' positions? If yes, list the moves.

Answer Format:
- For impossible puzzles: "No"
- For possible puzzles: List moves as ["color,from,to", ...]
  Example: ["w,A1,B3"] means white knight moves A1→B3

Answer: No
Metadata: {'board': {'C1': ['A2', 'B3', 'D3'], 'A2': ['C1'], 'B3': ['C1'], 'D1': ['B2'], 'B2': ['D1', 'D3'], 'D3': ['B2', 'C1']}, 'pieces': {'C1': 'B', 'A2': 'B', 'B3': None, 'D1': 'w', 'B2': 'w', 'D3': None}, 'start_turn': 'w', 'solution': None, 'is_possible': False, 'num_steps': 0, 'board_states': None}

Example 2:
Question: Knight Swap Challenge:

```
    A   B   C   D
   ----------------
3 |   | w | . |   |
   ----------------
2 | w |   |   | B |
   ----------------
1 |   |   | . | B |
   ----------------
```

Legend:
- 'w' = White Knight
- 'B' = Black Knight
- Empty squares are marked with '.'

Objective:
Swap the positions of all white knights with all black knights through valid moves.

Rules:
1. Knights move in L-shape (2 squares + 1 square perpendicular)
2. Knights can only move to empty squares
3. w moves first, then players alternate
4. All knights must reach their target positions (white ↔ black)

Question:
Is it possible to swap all knights' positions? If yes, list the moves.

Answer Format:
- For impossible puzzles: "No"
- For possible puzzles: List moves as ["color,from,to", ...]
  Example: ["w,A1,B3"] means white knight moves A1→B3

Answer: No
Metadata: {'board': {'B3': ['C1'], 'D1': ['C3'], 'C3': ['A2', 'D1'], 'C1': ['A2', 'B3'], 'D2': [], 'A2': ['C1', 'C3']}, 'pieces': {'B3': 'w', 'D1': 'B', 'C3': None, 'C1': None, 'D2': 'B', 'A2': 'w'}, 'start_turn': 'w', 'solution': None, 'is_possible': False, 'num_steps': 0, 'board_states': None}

Example 3:
Question: Knight Swap Challenge:

```
    A   B   C
   ------------
3 | . |   | B |
   ------------
2 | w |   | . |
   ------------
1 |   | w | B |
   ------------
```

Legend:
- 'w' = White Knight
- 'B' = Black Knight
- Empty squares are marked with '.'

Objective:
Swap the positions of all white knights with all black knights through valid moves.

Rules:
1. Knights move in L-shape (2 squares + 1 square perpendicular)
2. Knights can only move to empty squares
3. w moves first, then players alternate
4. All knights must reach their target positions (white ↔ black)

Question:
Is it possible to swap all knights' positions? If yes, list the moves.

Answer Format:
- For impossible puzzles: "No"
- For possible puzzles: List moves as ["color,from,to", ...]
  Example: ["w,A1,B3"] means white knight moves A1→B3

Answer: No
Metadata: {'board': {'B1': ['A3'], 'A3': ['B1', 'C2'], 'A2': ['C1', 'C3'], 'C3': ['A2'], 'C1': ['A2'], 'C2': ['A3']}, 'pieces': {'B1': 'w', 'A3': None, 'A2': 'w', 'C3': 'B', 'C1': 'B', 'C2': None}, 'start_turn': 'w', 'solution': None, 'is_possible': False, 'num_steps': 0, 'board_states': None}

largest_island

Generates Largest Island exercises with configurable difficulty

Default configuration:

rows = 10
cols = 10
max_num_islands = 5
max_island_size = 10
size = 500
seed = 42

Example tasks:

Example 1:
Question: You are given the following 10 x 10 binary matrix grid:
0 0 0 1 0 0 0 0 0 0
1 1 0 1 0 0 0 0 0 1
0 1 0 1 1 0 0 0 0 1
0 1 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 1 1
0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 1 0
1 1 0 1 1 0 0 0 1 1
1 1 1 1 1 0 0 0 0 0

An island is a group of 1's (representing land) connected 4-directionally (horizontal or vertical).
You may assume all four edges of the grid are surrounded by water.

The area of an island is the number of cells with a value 1 in the island.

Return the maximum area of an island in grid. If there is no island, return 0.

Answer: 10
Metadata: {'grid': [[0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 1, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [1, 1, 0, 1, 1, 0, 0, 0, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0, 0]], 'solution': 10}

Example 2:
Question: You are given the following 10 x 10 binary matrix grid:
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0

An island is a group of 1's (representing land) connected 4-directionally (horizontal or vertical).
You may assume all four edges of the grid are surrounded by water.

The area of an island is the number of cells with a value 1 in the island.

Return the maximum area of an island in grid. If there is no island, return 0.

Answer: 0
Metadata: {'grid': [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], 'solution': 0}

Example 3:
Question: You are given the following 10 x 10 binary matrix grid:
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0

An island is a group of 1's (representing land) connected 4-directionally (horizontal or vertical).
You may assume all four edges of the grid are surrounded by water.

The area of an island is the number of cells with a value 1 in the island.

Return the maximum area of an island in grid. If there is no island, return 0.

Answer: 3
Metadata: {'grid': [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], 'solution': 3}

lcm

Generates Least Common Multiple (LCM) tasks

Default configuration:

min_numbers = 2
max_numbers = 2
min_value = 1
max_value = 100
seed = 42
size = 500

Example tasks:

Example 1:
Question: Find the Least Common Multiple (LCM) of these numbers: 95, 14
Answer: 1330
Metadata: {'numbers': [95, 14], 'result': 1330}

Example 2:
Question: Find the Least Common Multiple (LCM) of these numbers: 60, 48
Answer: 240
Metadata: {'numbers': [60, 48], 'result': 240}

Example 3:
Question: Find the Least Common Multiple (LCM) of these numbers: 38, 4
Answer: 76
Metadata: {'numbers': [38, 4], 'result': 76}

leg_counting

Generates leg counting arithmetic tasks

Default configuration:

min_animals = 2
max_animals = 5
max_instances = 3
seed = 42
size = 500

Example tasks:

Example 1:
Question: How many legs are there in total if you have 1 sea slug, 1 deer?
Answer: 4
Metadata: {'difficulty': {'num_animals': 2}, 'animals': {'sea slug': 1, 'deer': 1}, 'total_legs': 4}

Example 2:
Question: How many legs are there in total if you have 2 sheeps, 2 dogs?
Answer: 16
Metadata: {'difficulty': {'num_animals': 2}, 'animals': {'sheep': 2, 'dog': 2}, 'total_legs': 16}

Example 3:
Question: How many legs are there in total if you have 1 crab, 2 lobsters, 1 human, 1 cow, 1 bee?
Answer: 42
Metadata: {'difficulty': {'num_animals': 5}, 'animals': {'crab': 1, 'lobster': 2, 'human': 1, 'cow': 1, 'bee': 1}, 'total_legs': 42}

letter_counting

Generates letter counting tasks from text spans

Default configuration:

min_words = 5
max_words = 15
seed = 42
size = 500

Example tasks:

Example 1:
Question: How many times does the letter "a" appear in the text: "bed and enters his mechanical dresser Two minutes later the machine deposited him all dressed"?
Answer: 6
Metadata: {'span_length': 15, 'target_letter': 'a', 'span': ['bed', 'and', 'enters', 'his', 'mechanical', 'dresser', 'Two', 'minutes', 'later', 'the', 'machine', 'deposited', 'him', 'all', 'dressed']}

Example 2:
Question: How many times does the letter "w" appear in the text: "it into a watering place"?
Answer: 1
Metadata: {'span_length': 5, 'target_letter': 'w', 'span': ['it', 'into', 'a', 'watering', 'place']}

Example 3:
Question: How many times does the letter "t" appear in the text: "readable form accessible by the widest array of equipment including outdated"?
Answer: 5
Metadata: {'span_length': 11, 'target_letter': 't', 'span': ['readable', 'form', 'accessible', 'by', 'the', 'widest', 'array', 'of', 'equipment', 'including', 'outdated']}

letter_jumble

Generates word letter jumbling tasks

Default configuration:

min_word_len = 1
max_word_len = 64
min_words = 3
max_words = 20
min_corruption_level = 0.1
max_corruption_level = 0.9
consecutive_words = True
seed = 42
size = 500

Example tasks:

Example 1:
Question: Unscramble these words: ew hsall eb ebla ot puodrce
Answer: we shall be able to produce
Metadata: {'num_words': 6, 'corruption_level': 0.12000860417813355, 'scrambled_words': ['ew', 'hsall', 'eb', 'ebla', 'ot', 'puodrce'], 'original_words': ['we', 'shall', 'be', 'able', 'to', 'produce']}

Example 2:
Question: Unscramble these words: ni oiurnalmsj Well Cahs
Answer: in journalism Well Cash
Metadata: {'num_words': 4, 'corruption_level': 0.3288673442377109, 'scrambled_words': ['ni', 'oiurnalmsj', 'Well', 'Cahs'], 'original_words': ['in', 'journalism', 'Well', 'Cash']}

Example 3:
Question: Unscramble these words: dear rchAdbali keep no nSice yrstyedae atnhks ot oyu rheet si a gain fo sucrbbisesr rM
Answer: dear Archibald keep on Since yesterday thanks to you there is a gain of subscribers Mr
Metadata: {'num_words': 16, 'corruption_level': 0.516016391169858, 'scrambled_words': ['dear', 'rchAdbali', 'keep', 'no', 'nSice', 'yrstyedae', 'atnhks', 'ot', 'oyu', 'rheet', 'si', 'a', 'gain', 'fo', 'sucrbbisesr', 'rM'], 'original_words': ['dear', 'Archibald', 'keep', 'on', 'Since', 'yesterday', 'thanks', 'to', 'you', 'there', 'is', 'a', 'gain', 'of', 'subscribers', 'Mr']}

manipulate_matrix

Generates Manipulate Matrix exercises with configurable difficulty

Default configuration:

min_rows = 1
min_cols = 1
max_rows = 10
max_cols = 10
max_transforms = 5
p_rotate = 0.2
p_hmirror = 0.2
p_vmirror = 0.2
p_dmirror = 0.2
p_cmirror = 0.2
p_map = 0.2
p_crop = 0.2
p_remove_every_nth_row = 0.2
p_remove_every_nth_col = 0.2
p_zero_divisible = 0.2
size = 500
seed = 42

Example tasks:

Example 1:
Question: For the following matrix:
4
3

Perform the following series of operations in order:
- Identity transformation, i.e. no change


Answer: 4
3
Metadata: {'matrix': [[4], [3]], 'solution': [[4], [3]], 'operations': []}

Example 2:
Question: For the following matrix:
2 7 5 1 7

Perform the following series of operations in order:
- Identity transformation, i.e. no change


Answer: 2 7 5 1 7
Metadata: {'matrix': [[2, 7, 5, 1, 7]], 'solution': [[2, 7, 5, 1, 7]], 'operations': []}

Example 3:
Question: For the following matrix:
8 1 2 6 3 4 0 3 1
9 0 1 2 8 4 6 9 6
5 5 1 5 4 9 2 1 8
1 9 1 4 5 1 4 0 5
6 1 7 7 3 3 2 4 3
0 0 6 0 5 5 7 7 9
8 2 3 7 7 5 9 0 4

Perform the following series of operations in order:
- Identity transformation, i.e. no change


Answer: 8 1 2 6 3 4 0 3 1
9 0 1 2 8 4 6 9 6
5 5 1 5 4 9 2 1 8
1 9 1 4 5 1 4 0 5
6 1 7 7 3 3 2 4 3
0 0 6 0 5 5 7 7 9
8 2 3 7 7 5 9 0 4
Metadata: {'matrix': [[8, 1, 2, 6, 3, 4, 0, 3, 1], [9, 0, 1, 2, 8, 4, 6, 9, 6], [5, 5, 1, 5, 4, 9, 2, 1, 8], [1, 9, 1, 4, 5, 1, 4, 0, 5], [6, 1, 7, 7, 3, 3, 2, 4, 3], [0, 0, 6, 0, 5, 5, 7, 7, 9], [8, 2, 3, 7, 7, 5, 9, 0, 4]], 'solution': [[8, 1, 2, 6, 3, 4, 0, 3, 1], [9, 0, 1, 2, 8, 4, 6, 9, 6], [5, 5, 1, 5, 4, 9, 2, 1, 8], [1, 9, 1, 4, 5, 1, 4, 0, 5], [6, 1, 7, 7, 3, 3, 2, 4, 3], [0, 0, 6, 0, 5, 5, 7, 7, 9], [8, 2, 3, 7, 7, 5, 9, 0, 4]], 'operations': []}

maze

Generates mazes with guaranteed shortest path distance from start to goal within [min_dist, max_dist].

Default configuration:

min_dist = 5
max_dist = 10
min_grid_size = 5
max_grid_size = 10
seed = 42
size = 50

Example tasks:

Example 1:
Question: Navigate from '3' (start) to 'z' (goal):

```
>>>>>>>>>
>eeee>e>>
>ee>>>>>>
>eeeeee>>
>e>ee>>e>
>>ez>3e>>
>eee>e>e>
>eeeee>e>
>>>>>>>>>
```
Legend: '>' = Wall, 'e' = Passage

What is the minimum number of steps to reach the goal?
Answer: 6
Metadata: {'grid_size': 9, 'grid': ['>>>>>>>>>', '>eeee>e>>', '>ee>>>>>>', '>eeeeee>>', '>e>ee>>e>', '>>ez>3e>>', '>eee>e>e>', '>eeeee>e>', '>>>>>>>>>'], 'shortest_path_length': 6, 'start': '3', 'goal': 'z', 'wall': '>', 'path': 'e'}

Example 2:
Question: Navigate from '`' (start) to 'i' (goal):

```
4444444
4AAAAi4
4A4A4A4
4A4AA44
44AAAA4
44A`444
4444444
```
Legend: '4' = Wall, 'A' = Passage

What is the minimum number of steps to reach the goal?
Answer: 6
Metadata: {'grid_size': 7, 'grid': ['4444444', '4AAAAi4', '4A4A4A4', '4A4AA44', '44AAAA4', '44A`444', '4444444'], 'shortest_path_length': 6, 'start': '`', 'goal': 'i', 'wall': '4', 'path': 'A'}

Example 3:
Question: Navigate from '(' (start) to '`' (goal):

```
QQQQQQQ
QQ%%%%Q
QQ`%Q%Q
Q%%Q%%Q
Q%%%Q%Q
Q%QQ%(Q
QQQQQQQ
```
Legend: 'Q' = Wall, '%' = Passage

What is the minimum number of steps to reach the goal?
Answer: 8
Metadata: {'grid_size': 7, 'grid': ['QQQQQQQ', 'QQ%%%%Q', 'QQ`%Q%Q', 'Q%%Q%%Q', 'Q%%%Q%Q', 'Q%QQ%(Q', 'QQQQQQQ'], 'shortest_path_length': 8, 'start': '(', 'goal': '`', 'wall': 'Q', 'path': '%'}

mini_sudoku

Generates 4x4 sudoku puzzles with configurable difficulty

Default configuration:

min_empty = 8
max_empty = 12
seed = 42
size = 500

Example tasks:

Example 1:
Question: Solve this 4x4 Mini Sudoku puzzle:
_ _ _ _
_ _ _ _
_ 1 3 _
_ 4 _ 1
Answer: 4 2 1 3
1 3 4 2
2 1 3 4
3 4 2 1
Metadata: {'puzzle': [[0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 3, 0], [0, 4, 0, 1]], 'solution': [[4, 2, 1, 3], [1, 3, 4, 2], [2, 1, 3, 4], [3, 4, 2, 1]], 'num_empty': 12}

Example 2:
Question: Solve this 4x4 Mini Sudoku puzzle:
3 _ _ _
_ _ 4 _
4 2 _ _
_ _ _ 4
Answer: 3 4 1 2
2 1 4 3
4 2 3 1
1 3 2 4
Metadata: {'puzzle': [[3, 0, 0, 0], [0, 0, 4, 0], [4, 2, 0, 0], [0, 0, 0, 4]], 'solution': [[3, 4, 1, 2], [2, 1, 4, 3], [4, 2, 3, 1], [1, 3, 2, 4]], 'num_empty': 11}

Example 3:
Question: Solve this 4x4 Mini Sudoku puzzle:
_ _ _ _
1 3 4 _
3 1 2 4
4 _ _ _
Answer: 2 4 1 3
1 3 4 2
3 1 2 4
4 2 3 1
Metadata: {'puzzle': [[0, 0, 0, 0], [1, 3, 4, 0], [3, 1, 2, 4], [4, 0, 0, 0]], 'solution': [[2, 4, 1, 3], [1, 3, 4, 2], [3, 1, 2, 4], [4, 2, 3, 1]], 'num_empty': 8}

n_queens

Generates N Queens puzzles with configurable difficulty

Default configuration:

n = 8
min_remove = 1
max_remove = 7
size = 500
seed = 42

Example tasks:

Example 1:
Question: Solve this N Queens puzzle:
_ _ _ _ _ _ Q _
_ Q _ _ _ _ _ _
_ _ _ Q _ _ _ _
_ _ _ _ _ _ _ _
_ _ _ _ _ _ _ Q
_ _ _ _ Q _ _ _
_ _ Q _ _ _ _ _
_ _ _ _ _ Q _ _

The board size is 8x8 and your job is to place 1 queen(s) on the board such that no two queens attack each other.

No two queens attack each other if they are not in the same row, column, or diagonal.

Place a queen by replacing an underscore (_) with a Q.

Answer: _ _ _ _ _ _ Q _
_ Q _ _ _ _ _ _
_ _ _ Q _ _ _ _
Q _ _ _ _ _ _ _
_ _ _ _ _ _ _ Q
_ _ _ _ Q _ _ _
_ _ Q _ _ _ _ _
_ _ _ _ _ Q _ _
Metadata: {'puzzle': [['_', '_', '_', '_', '_', '_', 'Q', '_'], ['_', 'Q', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', 'Q', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', '_', '_', 'Q'], ['_', '_', '_', '_', 'Q', '_', '_', '_'], ['_', '_', 'Q', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', 'Q', '_', '_']], 'solutions': [[['_', '_', '_', '_', '_', '_', 'Q', '_'], ['_', 'Q', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', 'Q', '_', '_', '_', '_'], ['Q', '_', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', '_', '_', 'Q'], ['_', '_', '_', '_', 'Q', '_', '_', '_'], ['_', '_', 'Q', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', 'Q', '_', '_']]], 'num_removed': 1, 'valid_answers': ['_ _ _ _ _ _ Q _\n_ Q _ _ _ _ _ _\n_ _ _ Q _ _ _ _\nQ _ _ _ _ _ _ _\n_ _ _ _ _ _ _ Q\n_ _ _ _ Q _ _ _\n_ _ Q _ _ _ _ _\n_ _ _ _ _ Q _ _']}

Example 2:
Question: Solve this N Queens puzzle:
_ Q _ _ _ _ _ _
_ _ _ _ _ _ _ _
_ _ _ _ _ Q _ _
_ _ _ _ _ _ _ Q
_ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _
_ _ _ _ _ _ Q _
_ _ _ _ Q _ _ _

The board size is 8x8 and your job is to place 3 queen(s) on the board such that no two queens attack each other.

No two queens attack each other if they are not in the same row, column, or diagonal.

Place a queen by replacing an underscore (_) with a Q.

Answer: _ Q _ _ _ _ _ _
_ _ _ Q _ _ _ _
_ _ _ _ _ Q _ _
_ _ _ _ _ _ _ Q
_ _ Q _ _ _ _ _
Q _ _ _ _ _ _ _
_ _ _ _ _ _ Q _
_ _ _ _ Q _ _ _
Metadata: {'puzzle': [['_', 'Q', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', 'Q', '_', '_'], ['_', '_', '_', '_', '_', '_', '_', 'Q'], ['_', '_', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', '_', 'Q', '_'], ['_', '_', '_', '_', 'Q', '_', '_', '_']], 'solutions': [[['_', 'Q', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', 'Q', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', 'Q', '_', '_'], ['_', '_', '_', '_', '_', '_', '_', 'Q'], ['_', '_', 'Q', '_', '_', '_', '_', '_'], ['Q', '_', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', '_', 'Q', '_'], ['_', '_', '_', '_', 'Q', '_', '_', '_']]], 'num_removed': 3, 'valid_answers': ['_ Q _ _ _ _ _ _\n_ _ _ Q _ _ _ _\n_ _ _ _ _ Q _ _\n_ _ _ _ _ _ _ Q\n_ _ Q _ _ _ _ _\nQ _ _ _ _ _ _ _\n_ _ _ _ _ _ Q _\n_ _ _ _ Q _ _ _']}

Example 3:
Question: Solve this N Queens puzzle:
_ _ _ _ _ _ _ _
_ Q _ _ _ _ _ _
_ _ _ _ _ _ _ _
Q _ _ _ _ _ _ _
_ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _
_ _ _ _ _ Q _ _

The board size is 8x8 and your job is to place 5 queen(s) on the board such that no two queens attack each other.

No two queens attack each other if they are not in the same row, column, or diagonal.

Place a queen by replacing an underscore (_) with a Q.

Answer: _ _ _ _ Q _ _ _
_ Q _ _ _ _ _ _
_ _ _ _ _ _ _ Q
Q _ _ _ _ _ _ _
_ _ _ Q _ _ _ _
_ _ _ _ _ _ Q _
_ _ Q _ _ _ _ _
_ _ _ _ _ Q _ _
Metadata: {'puzzle': [['_', '_', '_', '_', '_', '_', '_', '_'], ['_', 'Q', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', '_', '_', '_'], ['Q', '_', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', 'Q', '_', '_']], 'solutions': [[['_', '_', '_', '_', 'Q', '_', '_', '_'], ['_', 'Q', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', '_', '_', 'Q'], ['Q', '_', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', 'Q', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', '_', 'Q', '_'], ['_', '_', 'Q', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', 'Q', '_', '_']], [['_', '_', '_', '_', '_', '_', 'Q', '_'], ['_', 'Q', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', 'Q', '_', '_', '_', '_'], ['Q', '_', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', '_', '_', 'Q'], ['_', '_', '_', '_', 'Q', '_', '_', '_'], ['_', '_', 'Q', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', 'Q', '_', '_']], [['_', '_', '_', '_', '_', '_', '_', 'Q'], ['_', 'Q', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', 'Q', '_', '_', '_', '_'], ['Q', '_', '_', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', '_', 'Q', '_'], ['_', '_', '_', '_', 'Q', '_', '_', '_'], ['_', '_', 'Q', '_', '_', '_', '_', '_'], ['_', '_', '_', '_', '_', 'Q', '_', '_']]], 'num_removed': 5, 'valid_answers': ['_ _ _ _ Q _ _ _\n_ Q _ _ _ _ _ _\n_ _ _ _ _ _ _ Q\nQ _ _ _ _ _ _ _\n_ _ _ Q _ _ _ _\n_ _ _ _ _ _ Q _\n_ _ Q _ _ _ _ _\n_ _ _ _ _ Q _ _', '_ _ _ _ _ _ Q _\n_ Q _ _ _ _ _ _\n_ _ _ Q _ _ _ _\nQ _ _ _ _ _ _ _\n_ _ _ _ _ _ _ Q\n_ _ _ _ Q _ _ _\n_ _ Q _ _ _ _ _\n_ _ _ _ _ Q _ _', '_ _ _ _ _ _ _ Q\n_ Q _ _ _ _ _ _\n_ _ _ Q _ _ _ _\nQ _ _ _ _ _ _ _\n_ _ _ _ _ _ Q _\n_ _ _ _ Q _ _ _\n_ _ Q _ _ _ _ _\n_ _ _ _ _ Q _ _']}

number_filtering

Generates number filtering tasks

Default configuration:

min_numbers = 3
max_numbers = 10
min_decimals = 0
max_decimals = 4
min_value = -100.0
max_value = 100.0
seed = 42
size = 500

Example tasks:

Example 1:
Question: Keep all numbers larger than -90 in this list: ['-95.00', '-51.0', '47.2942', '-82.612']
Return the new list in the same format.
Answer: ['-51.0', '47.2942', '-82.612']
Metadata: {'original_numbers': ['-95.00', '-51.0', '47.2942', '-82.612'], 'filter_value': '-90', 'operation': 'keep_larger', 'result': ['-51.0', '47.2942', '-82.612']}

Example 2:
Question: Remove all numbers larger than 18.236 in this list: ['-42.8', '91.88', '34']
Return the new list in the same format.
Answer: ['-42.8']
Metadata: {'original_numbers': ['-42.8', '91.88', '34'], 'filter_value': '18.236', 'operation': 'remove_larger', 'result': ['-42.8']}

Example 3:
Question: Keep all numbers larger than 19.8962 in this list: ['4', '-64.7', '-42.1', '-77', '-79.9640', '37.76', '38.702', '18.20', '-28.34']
Return the new list in the same format.
Answer: ['37.76', '38.702']
Metadata: {'original_numbers': ['4', '-64.7', '-42.1', '-77', '-79.9640', '37.76', '38.702', '18.20', '-28.34'], 'filter_value': '19.8962', 'operation': 'keep_larger', 'result': ['37.76', '38.702']}

number_sequence

Generates number sequence completion tasks with dynamic pattern generation

Default configuration:

min_terms = 4
max_terms = 8
min_value = -100
max_value = 100
max_complexity = 3
seed = 42
size = 500

Example tasks:

Example 1:
Question: 3, 6, 12, 24, 48, 96, 192, 384, ?
Answer: 768
Metadata: {'rule': 'double', 'complexity': 3, 'sequence': [3, 6, 12, 24, 48, 96, 192, 384, 768]}

Example 2:
Question: 8, 14, 20, 26, 32, 38, 44, ?
Answer: 50
Metadata: {'rule': 'add 6', 'complexity': 1, 'sequence': [8, 14, 20, 26, 32, 38, 44, 50]}

Example 3:
Question: 8, 4, 2, 1, 0, 0, 0, ?
Answer: 0
Metadata: {'rule': 'halve', 'complexity': 2, 'sequence': [8, 4, 2, 1, 0, 0, 0, 0]}

number_sorting

Generates number sorting tasks

Default configuration:

min_numbers = 3
max_numbers = 10
min_decimals = 0
max_decimals = 2
min_value = -100.0
max_value = 100.0
seed = 42
size = 500

Example tasks:

Example 1:
Question: Sort these numbers in ascending order: 48, -51, -72, -80
Please follow the instruction below:
## 1. Let all your answers be a list of numbers. Instead of reporting your answer as -69, -13, 1, 7, 11, 43, 59, 61, use ['-69', '-13', '1', '7', '11', '43', '59', '61'] instead
## 2. Convert all numbers in the square brackets as strings. For example, ['-69', '-13', '1', '7', '11', '43', '59', '61']

Answer: ['-80', '-72', '-51', '48']
Metadata: {'original_numbers': ['48', '-51', '-72', '-80'], 'direction': 'ascending', 'sorted_numbers': ['-80', '-72', '-51', '48']}

Example 2:
Question: Sort these numbers in ascending order: 39.2, -71.2, -7.5
Please follow the instruction below:
## 1. Let all your answers be a list of numbers. Instead of reporting your answer as -69, -13, 1, 7, 11, 43, 59, 61, use ['-69', '-13', '1', '7', '11', '43', '59', '61'] instead
## 2. Convert all numbers in the square brackets as strings. For example, ['-69', '-13', '1', '7', '11', '43', '59', '61']

Answer: ['-71.2', '-7.5', '39.2']
Metadata: {'original_numbers': ['39.2', '-71.2', '-7.5'], 'direction': 'ascending', 'sorted_numbers': ['-71.2', '-7.5', '39.2']}

Example 3:
Question: Sort these numbers in descending order: 8.39, 72.41, -64.67, -54.97, -94.18, -76.67, -98.24, -68.66, 2.74
Please follow the instruction below:
## 1. Let all your answers be a list of numbers. Instead of reporting your answer as -69, -13, 1, 7, 11, 43, 59, 61, use ['-69', '-13', '1', '7', '11', '43', '59', '61'] instead
## 2. Convert all numbers in the square brackets as strings. For example, ['-69', '-13', '1', '7', '11', '43', '59', '61']

Answer: ['72.41', '8.39', '2.74', '-54.97', '-64.67', '-68.66', '-76.67', '-94.18', '-98.24']
Metadata: {'original_numbers': ['8.39', '72.41', '-64.67', '-54.97', '-94.18', '-76.67', '-98.24', '-68.66', '2.74'], 'direction': 'descending', 'sorted_numbers': ['72.41', '8.39', '2.74', '-54.97', '-64.67', '-68.66', '-76.67', '-94.18', '-98.24']}

palindrome

Generates a set of letters that can be assembled into a palindrome.

Default configuration:

min_length = 3
max_length = 10
seed = 42
size = 50

Example tasks:

Example 1:
Question: Rearrange these letters to form a palindrome. A palindrome is a word, phrase, or sequence that reads the same forward and backward.

For example, if the letters are: a, a, b — a valid palindrome is: aba.

Your letters: h, a, h, a

What palindrome can you form from these letters?
Answer: ahha
Metadata: {'letters': ['h', 'a', 'h', 'a'], 'generated_palindrome': 'ahha'}

Example 2:
Question: Rearrange these letters to form a palindrome. A palindrome is a word, phrase, or sequence that reads the same forward and backward.

For example, if the letters are: a, a, b — a valid palindrome is: aba.

Your letters: h, y, h

What palindrome can you form from these letters?
Answer: hyh
Metadata: {'letters': ['h', 'y', 'h'], 'generated_palindrome': 'hyh'}

Example 3:
Question: Rearrange these letters to form a palindrome. A palindrome is a word, phrase, or sequence that reads the same forward and backward.

For example, if the letters are: a, a, b — a valid palindrome is: aba.

Your letters: n, j, n, j, d, j, s, s, d

What palindrome can you form from these letters?
Answer: nsdjjjdsn
Metadata: {'letters': ['n', 'j', 'n', 'j', 'd', 'j', 's', 's', 'd'], 'generated_palindrome': 'nsdjjjdsn'}

polynomial_equations

Generates random polynomial equations of degree in [min_degree, max_degree]. - The polynomial is formed by summing random terms of the form: coeff * x^exponent. - Then we solve "polynomial_expr = 0" using Sympy. - The solution may be real or complex; we filter real solutions by default for simplicity.

Default configuration:

min_terms = 2
max_terms = 4
min_value = 1
max_value = 100
min_degree = 1
max_degree = 3
operators = ('+', '-')
seed = 42
size = 500

Example tasks:

Example 1:
Question: Find the real value(s) of w in the equation: -127*w = 0
In solving the equations, please abide by the following instruction:
## 1. All answers should be comma-separated. For example "-0.3773, 0.4005" etc.
## 2. In cases where your answer is b = 2 + sqrt(4560) / 172 and b = 2 - sqrt(4560) / 172. Since b can be 2 numbers, resolve your answer like this instead, "-0.3773, 0.4005".
## 3. If there are no real values of i that satisfy the equation, report your answer as empty string, "".
## 4. If there are 2 answers, resolve the answers as comma-separated floats of 2 numbers, if 3 answers, make it comma-separated floats of 3 numbers.
## 5. Resolve all numbers as floats in the string of comma-separated numbers. Round the floats higher than 4 decimal place(d.p) down to 4 d.p.

Answer: 0.0
Metadata: {'polynomial_expr': '-127*w', 'variable': 'w', 'degree': 1, 'real_solutions': [0.0]}

Example 2:
Question: Determine the real value(s) of b that satisfies: 86*b**2 - 2*b - 13 = 0
In solving the equations, please abide by the following instruction:
## 1. All answers should be comma-separated. For example "-0.3773, 0.4005" etc.
## 2. In cases where your answer is b = 2 + sqrt(4560) / 172 and b = 2 - sqrt(4560) / 172. Since b can be 2 numbers, resolve your answer like this instead, "-0.3773, 0.4005".
## 3. If there are no real values of i that satisfy the equation, report your answer as empty string, "".
## 4. If there are 2 answers, resolve the answers as comma-separated floats of 2 numbers, if 3 answers, make it comma-separated floats of 3 numbers.
## 5. Resolve all numbers as floats in the string of comma-separated numbers. Round the floats higher than 4 decimal place(d.p) down to 4 d.p.

Answer: -0.3773, 0.4006
Metadata: {'polynomial_expr': '86*b**2 - 2*b - 13', 'variable': 'b', 'degree': 2, 'real_solutions': [-0.3773, 0.4006]}

Example 3:
Question: Determine the real value(s) of p that satisfies: 71*p**3 - 2*p - 29 = 0
In solving the equations, please abide by the following instruction:
## 1. All answers should be comma-separated. For example "-0.3773, 0.4005" etc.
## 2. In cases where your answer is b = 2 + sqrt(4560) / 172 and b = 2 - sqrt(4560) / 172. Since b can be 2 numbers, resolve your answer like this instead, "-0.3773, 0.4005".
## 3. If there are no real values of i that satisfy the equation, report your answer as empty string, "".
## 4. If there are 2 answers, resolve the answers as comma-separated floats of 2 numbers, if 3 answers, make it comma-separated floats of 3 numbers.
## 5. Resolve all numbers as floats in the string of comma-separated numbers. Round the floats higher than 4 decimal place(d.p) down to 4 d.p.

Answer: 0.7546
Metadata: {'polynomial_expr': '71*p**3 - 2*p - 29', 'variable': 'p', 'degree': 3, 'real_solutions': [0.7546]}

polynomial_multiplication

Generates [min_polynomials, max_polynomials] random polynomials of degree in [min_degree, max_degree]. - The polynomial is formed by summing random terms of the form: coeff * x^exponent. - Then we find "F = P_0 * ... * P_1" using Sympy.

Default configuration:

min_terms = 2
max_terms = 4
min_value = 1
max_value = 100
min_degree = 1
max_degree = 3
min_polynomials = 2
max_polynomials = 3
single_variable = True
operators = ('+', '-')
seed = 42
size = 500

Example tasks:

Example 1:
Question: Calculate the following: (65*x - 72)*(105*x - 125)
In addition, When doing calculation, Use the following instructions together with your mathematical ingenuity to solve the integral problems
## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
## 2. Always use * when doing all sorts of multiplcation in your reasoning steps and even in reporting answers.

Answer: 6825*x**2 - 15685*x + 9000
Metadata: {'polynomial_expr': '(65*x - 72)*(105*x - 125)', 'single_variable': True, 'result': '6825*x**2 - 15685*x + 9000'}

Example 2:
Question: Calculate the following: (-9*x**2 - 28*x)*(86*x**2 - 2*x - 13)
In addition, When doing calculation, Use the following instructions together with your mathematical ingenuity to solve the integral problems
## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
## 2. Always use * when doing all sorts of multiplcation in your reasoning steps and even in reporting answers.

Answer: -774*x**4 - 2390*x**3 + 173*x**2 + 364*x
Metadata: {'polynomial_expr': '(-9*x**2 - 28*x)*(86*x**2 - 2*x - 13)', 'single_variable': True, 'result': '-774*x**4 - 2390*x**3 + 173*x**2 + 364*x'}

Example 3:
Question: Calculate the following: (43 - 91*x)*(3*x**2 - 10*x)*(71*x**3 - 2*x - 29)
In addition, When doing calculation, Use the following instructions together with your mathematical ingenuity to solve the integral problems
## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
## 2. Always use * when doing all sorts of multiplcation in your reasoning steps and even in reporting answers.

Answer: -19383*x**6 + 73769*x**5 - 29984*x**4 + 5839*x**3 - 29271*x**2 + 12470*x
Metadata: {'polynomial_expr': '(43 - 91*x)*(3*x**2 - 10*x)*(71*x**3 - 2*x - 29)', 'single_variable': True, 'result': '-19383*x**6 + 73769*x**5 - 29984*x**4 + 5839*x**3 - 29271*x**2 + 12470*x'}

pool_matrix

Generates Pool Matrix exercises with configurable difficulty

Default configuration:

min_rows = 2
min_cols = 2
max_rows = 10
max_cols = 10
max_pool_size = 3
size = 500
seed = 42

Example tasks:

Example 1:
Question: Your job is to perform max/average pooling on the given matrix.
The stride is equal to the kernel size, meaning there is no overlap between the pooling regions.

Example 1:
- Input: Perform max pooling on the following matrix with a kernel size of 2:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
- Output:
6 8
14 16

Example 2:
- Input: Perform average pooling on the following matrix with a kernel size of 2:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
- Output:
3.5 5.5
11.5 13.5

Perform max pooling on the following matrix with a kernel size of 3:
6 3
7 4
6 9

Answer: 9
Metadata: {'matrix': [[6, 3], [7, 4], [6, 9]], 'pool_type': 'max', 'pool_size': 3, 'solution': [[9]]}

Example 2:
Question: Your job is to perform max/average pooling on the given matrix.
The stride is equal to the kernel size, meaning there is no overlap between the pooling regions.

Example 1:
- Input: Perform max pooling on the following matrix with a kernel size of 2:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
- Output:
6 8
14 16

Example 2:
- Input: Perform average pooling on the following matrix with a kernel size of 2:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
- Output:
3.5 5.5
11.5 13.5

Perform average pooling on the following matrix with a kernel size of 3:
4 0 1 5 0 3
1 2 7 0 3 2

Answer: 2.5 2.17
Metadata: {'matrix': [[4, 0, 1, 5, 0, 3], [1, 2, 7, 0, 3, 2]], 'pool_type': 'average', 'pool_size': 3, 'solution': [[2.5, 2.1666666666666665]]}

Example 3:
Question: Your job is to perform max/average pooling on the given matrix.
The stride is equal to the kernel size, meaning there is no overlap between the pooling regions.

Example 1:
- Input: Perform max pooling on the following matrix with a kernel size of 2:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
- Output:
6 8
14 16

Example 2:
- Input: Perform average pooling on the following matrix with a kernel size of 2:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
- Output:
3.5 5.5
11.5 13.5

Perform average pooling on the following matrix with a kernel size of 3:
4 3 1 3 0 4 3 8 7 7
6 9 3 7 3 3 6 5 4 5
9 1 8 7 4 5 3 0 4 9
2 8 8 6 2 0 3 4 8 3
2 2 1 2 2 9 8 1 8 9
4 2 4 6 7 5 5 6 2 5
1 8 9 1 8 0 9 3 5 9
5 0 8 0 4 2 9 7 6 6

Answer: 4.89 4.0 4.44 7.0
3.67 4.33 5.0 5.67
5.17 2.5 6.5 7.5
Metadata: {'matrix': [[4, 3, 1, 3, 0, 4, 3, 8, 7, 7], [6, 9, 3, 7, 3, 3, 6, 5, 4, 5], [9, 1, 8, 7, 4, 5, 3, 0, 4, 9], [2, 8, 8, 6, 2, 0, 3, 4, 8, 3], [2, 2, 1, 2, 2, 9, 8, 1, 8, 9], [4, 2, 4, 6, 7, 5, 5, 6, 2, 5], [1, 8, 9, 1, 8, 0, 9, 3, 5, 9], [5, 0, 8, 0, 4, 2, 9, 7, 6, 6]], 'pool_type': 'average', 'pool_size': 3, 'solution': [[4.888888888888889, 4.0, 4.444444444444445, 7.0], [3.6666666666666665, 4.333333333333333, 5.0, 5.666666666666667], [5.166666666666667, 2.5, 6.5, 7.5]]}

power_function

Generates Power Function exercises with configurable difficulty

Default configuration:

min_base = -1000.0
max_base = 1000.0
min_exponent = -8
max_exponent = 8
size = 500
seed = 42

Example tasks:

Example 1:
Question: Compute 278.8535969157674^-8
Answer: 2.735205704728613e-20
Metadata: {'base': 278.8535969157674, 'exponent': -8, 'solution': 2.735205704728613e-20}

Example 2:
Question: Compute -922.8963213252399^-4
Answer: 1.3784415023500506e-12
Metadata: {'base': -922.8963213252399, 'exponent': -4, 'solution': 1.3784415023500506e-12}

Example 3:
Question: Compute -182.9282414910125^-5
Answer: -4.881982323540115e-12
Metadata: {'base': -182.9282414910125, 'exponent': -5, 'solution': -4.881982323540115e-12}

prime_factorization

Generates prime factorization tasks

Default configuration:

min_value = 2
max_value = 1000
seed = 42
size = 500

Example tasks:

Example 1:
Question: Find the prime factorization of 656. Write the factors separated by × (Example: for 12 the answer would be: 2 × 2 × 3)
Answer: 2 × 2 × 2 × 2 × 41
Metadata: {'number': 656, 'factors': [2, 2, 2, 2, 41]}

Example 2:
Question: Find the prime factorization of 41. Write the factors separated by × (Example: for 12 the answer would be: 2 × 2 × 3)
Answer: 41
Metadata: {'number': 41, 'factors': [41]}

Example 3:
Question: Find the prime factorization of 420. Write the factors separated by × (Example: for 12 the answer would be: 2 × 2 × 3)
Answer: 2 × 2 × 3 × 5 × 7
Metadata: {'number': 420, 'factors': [2, 2, 3, 5, 7]}

products

Generates multiplication tasks with configurable number of terms

Default configuration:

min_terms = 2
max_terms = 2
min_digits = 1
max_digits = 5
seed = 42
size = 500

Example tasks:

Example 1:
Question: 4 * 3 =
Answer: 12
Metadata: {'difficulty': {'num_terms': 2, 'num_digits': 1}, 'expression': '4 * 3'}

Example 2:
Question: 812 * 880 =
Answer: 714560
Metadata: {'difficulty': {'num_terms': 2, 'num_digits': 3}, 'expression': '812 * 880'}

Example 3:
Question: 81037 * 25290 =
Answer: 2049425730
Metadata: {'difficulty': {'num_terms': 2, 'num_digits': 5}, 'expression': '81037 * 25290'}

propositional_logic

Generates propositional logic reasoning tasks

Default configuration:

min_vars = 2
max_vars = 4
min_statements = 2
max_statements = 4
max_complexity = 3
seed = 42
size = 500

Example tasks:

Example 1:
Question: Given:
1. R
2. Q
What can we conclude?
Answer: (P ∨ Q)
Metadata: {'premises': ['R', 'Q'], 'variables': ['P', 'Q', 'R', 'S'], 'complexity': 3}

Example 2:
Question: Given:
1. ((Q → P) ∨ (Q → P))
2. ((Q ↔ Q) → (P → P))
3. P
What can we conclude?
Answer: (P → P)
Metadata: {'premises': ['((Q → P) ∨ (Q → P))', '((Q ↔ Q) → (P → P))', 'P'], 'variables': ['P', 'Q'], 'complexity': 3}

Example 3:
Question: Given:
1. ((Q ∨ P) ∧ ¬P)
2. P
3. ((P ∧ R) ∧ ¬R)
4. ((Q ↔ R) → ¬Q)
What can we conclude?
Answer: (Q ∧ Q)
Metadata: {'premises': ['((Q ∨ P) ∧ ¬P)', 'P', '((P ∧ R) ∧ ¬R)', '((Q ↔ R) → ¬Q)'], 'variables': ['P', 'Q', 'R'], 'complexity': 3}

quantum_lock

Generates QuantumLock tasks

Default configuration:

difficulty = 10
seed = 42
size = 500

Example tasks:

Example 1:
Question: In front of you are some buttons, a light, and a number. The light will toggle between red and green whenever you press a button. Each button performs a mathematical operation to the number, but the operation may depend on the state of the light.
You must press the shortest correct sequence of buttons to reach the target value. Your answer should be a sequence of buttons separated by '→', for example: A → B → C

Start: 0 (red)
Target: 46
Buttons:
A: Add 3 (when any)
B: Add 2 (when any)
C: Multiply 2 (when any)
Answer: A → B → C → C → A → C
Metadata: {'difficulty': 10, 'solution_path': ['A', 'B', 'C', 'C', 'A', 'C'], 'target_value': 46, 'buttons': [{'name': 'A', 'type': 'add', 'value': 3, 'active_state': 'any'}, {'name': 'B', 'type': 'add', 'value': 2, 'active_state': 'any'}, {'name': 'C', 'type': 'multiply', 'value': 2, 'active_state': 'any'}], 'initial_state': 'red', 'initial_value': 0}

Example 2:
Question: In front of you are some buttons, a light, and a number. The light will toggle between red and green whenever you press a button. Each button performs a mathematical operation to the number, but the operation may depend on the state of the light.
You must press the shortest correct sequence of buttons to reach the target value. Your answer should be a sequence of buttons separated by '→', for example: A → B → C

Start: 0 (red)
Target: 30
Buttons:
A: Add 2 (when green)
B: Subtract 3 (when red)
C: Multiply 2 (when red)
Answer: C → A → C → A → C → A → C → A
Metadata: {'difficulty': 10, 'solution_path': ['C', 'A', 'C', 'A', 'C', 'A', 'C', 'A'], 'target_value': 30, 'buttons': [{'name': 'A', 'type': 'add', 'value': 2, 'active_state': 'green'}, {'name': 'B', 'type': 'subtract', 'value': 3, 'active_state': 'red'}, {'name': 'C', 'type': 'multiply', 'value': 2, 'active_state': 'red'}], 'initial_state': 'red', 'initial_value': 0}

Example 3:
Question: In front of you are some buttons, a light, and a number. The light will toggle between red and green whenever you press a button. Each button performs a mathematical operation to the number, but the operation may depend on the state of the light.
You must press the shortest correct sequence of buttons to reach the target value. Your answer should be a sequence of buttons separated by '→', for example: A → B → C

Start: 0 (red)
Target: 45
Buttons:
A: Subtract 2 (when any)
B: Add 3 (when any)
C: Add 2 (when any)
Answer: B → B → B → B → B → B → B → B → B → B → B → B → B → B → B
Metadata: {'difficulty': 10, 'solution_path': ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], 'target_value': 45, 'buttons': [{'name': 'A', 'type': 'subtract', 'value': 2, 'active_state': 'any'}, {'name': 'B', 'type': 'add', 'value': 3, 'active_state': 'any'}, {'name': 'C', 'type': 'add', 'value': 2, 'active_state': 'any'}], 'initial_state': 'red', 'initial_value': 0}

ransom_note

Generates Ransom Note exercises with configurable difficulty

Default configuration:

max_note_length = 10
max_magazine_length = 30
p_solvable = 0.5
size = 500
seed = 42

Example tasks:

Example 1:
Question: Given two strings representing a ransom note and a magazine, return True if you can construct the ransom note using the letters in the magazine, and False otherwise.

Each letter in the magazine string can only be used once in your ransom note.

Ransom note: c
Magazine: kjjfnerbv

Answer: False
Metadata: {'ransom_note': 'c', 'magazine': 'kjjfnerbv', 'solution': False, 'solvable': False}

Example 2:
Question: Given two strings representing a ransom note and a magazine, return True if you can construct the ransom note using the letters in the magazine, and False otherwise.

Each letter in the magazine string can only be used once in your ransom note.

Ransom note: pan
Magazine: pipmrxluyrkumtnaynmqosywf

Answer: True
Metadata: {'ransom_note': 'pan', 'magazine': 'pipmrxluyrkumtnaynmqosywf', 'solution': True, 'solvable': True}

Example 3:
Question: Given two strings representing a ransom note and a magazine, return True if you can construct the ransom note using the letters in the magazine, and False otherwise.

Each letter in the magazine string can only be used once in your ransom note.

Ransom note: yuothygge
Magazine: gpfslbehhhhagoutvejfoytuuyy

Answer: True
Metadata: {'ransom_note': 'yuothygge', 'magazine': 'gpfslbehhhhagoutvejfoytuuyy', 'solution': True, 'solvable': True}

rearc

Default configuration:

min_examples = 3
max_examples = 5
diff_lb = 0
diff_ub = 0.2
board_format_opts = BoardFormattingOptions(alphabet=['0', '1', '2', '3', '4', '5', '6', '7', '8', '9'], col_delimiter=' ', row_delimiter='\n', array_brackets=False)
seed = 42
size = 500

Example tasks:

Example 1:
Question: Find the common rule that maps an input grid to an output grid, given the examples below.

Example 1:

Input:
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 9
Output:
9 9 9 9
1 1 1 1
9 9 9 9
1 1 1 1
1 9 9 9
1 9 1 1
1 9 1 9

Example 2:

Input:
4 8 8 8 8 8 8
8 8 8 8 8 8 8
8 8 8 8 8 8 8
8 8 8 8 8 8 8
8 8 8 8 8 8 8
Output:
4 8 4 8 4 8 4
8 8 4 8 4 8 4
4 4 4 8 4 8 4
8 8 8 8 4 8 4
4 4 4 4 4 8 4

Example 3:

Input:
2 2 2 2
2 2 2 2
2 2 2 2
2 2 2 2
2 2 2 2
2 2 2 2
2 2 2 2
5 2 2 2
Output:
2 2 2 2
5 5 5 5
2 2 2 2
5 5 5 5
2 2 2 2
5 5 5 2
2 2 5 2
5 2 5 2


Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Your final answer should just be the text output grid itself.

Input:
3 3 3 3 3 3 3 9
3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3

Answer: 3 9 3 9 3 9 3 9
3 9 3 9 3 9 3 3
3 9 3 9 3 9 9 9
3 9 3 9 3 3 3 3
3 9 3 9 9 9 9 9
Metadata: {'input': ((3, 3, 3, 3, 3, 3, 3, 9), (3, 3, 3, 3, 3, 3, 3, 3), (3, 3, 3, 3, 3, 3, 3, 3), (3, 3, 3, 3, 3, 3, 3, 3), (3, 3, 3, 3, 3, 3, 3, 3)), 'output': ((3, 9, 3, 9, 3, 9, 3, 9), (3, 9, 3, 9, 3, 9, 3, 3), (3, 9, 3, 9, 3, 9, 9, 9), (3, 9, 3, 9, 3, 3, 3, 3), (3, 9, 3, 9, 9, 9, 9, 9)), 'task_id': 'd22278a0', 'difficulty': {'rng': 0.07173948707162241, 'pso': 0.12314814814814816}}

Example 2:
Question: Find the common rule that maps an input grid to an output grid, given the examples below.

Example 1:

Input:
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 9 6 6 6 9 6
6 6 6 9 6 9 6 6
6 6 6 6 9 6 6 6
6 6 6 9 6 9 6 6
6 6 9 6 6 6 9 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
Output:
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 9 6 6 6 9 6
6 6 6 9 6 9 6 6
6 6 6 6 9 6 6 6
6 6 6 9 6 9 6 6
6 6 9 6 6 6 9 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6

Example 2:

Input:
5 5 5 5 5 5 5 5 5 5
5 5 8 5 8 5 8 5 5 5
5 5 5 5 5 5 5 5 5 5
5 5 8 5 2 5 8 5 5 5
5 5 5 5 5 5 5 5 5 5
5 5 8 5 8 5 8 5 5 5
5 5 5 5 5 5 5 5 5 5
Output:
5 5 5 5 5 5 5 5 5 5
5 5 8 5 8 5 8 5 5 5
5 5 5 5 5 5 5 5 5 5
5 5 8 5 2 5 8 5 5 5
5 5 5 5 5 5 5 5 5 5
5 5 8 5 8 5 8 5 5 5
5 5 5 5 5 5 5 5 5 5

Example 3:

Input:
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 2 1 2 1 1 1
1 1 1 1 2 1 1 1 1
1 1 1 2 1 2 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
Output:
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 2 1 2 1 1 1
1 1 1 1 2 1 1 1 1
1 1 1 2 1 2 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1

Example 4:

Input:
7 7 7 7 7 7 7 7 7 7
7 7 7 1 7 1 7 1 7 7
7 7 7 7 7 7 7 7 7 7
7 7 7 1 7 1 7 1 7 7
7 7 7 7 7 7 7 7 7 7
7 7 7 1 7 1 7 1 7 7
7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7
Output:
7 7 7 7 7 7 7 7 7 7
7 7 7 1 7 1 7 1 7 7
7 7 7 7 7 7 7 7 7 7
7 7 7 1 7 1 7 1 7 7
7 7 7 7 7 7 7 7 7 7
7 7 7 1 7 1 7 1 7 7
7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7

Example 5:

Input:
3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 6 3 3 3 6 3 3
3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 6 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 6 3 3 3 6 3 3
3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3
Output:
3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 6 3 3 3 6 3 3
3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 6 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 6 3 3 3 6 3 3
3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3


Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Your final answer should just be the text output grid itself.

Input:
7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 8 7 7 7
7 7 7 7 7 7 8 7 8 7 7
7 7 7 7 7 8 7 8 7 8 7
7 7 7 7 7 7 8 7 8 7 7
7 7 7 7 7 7 7 8 7 7 7
7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7

Answer: 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 8 7 7 7
7 7 7 7 7 7 8 7 8 7 7
7 7 7 7 7 8 7 8 7 8 7
7 7 7 7 7 7 8 7 8 7 7
7 7 7 7 7 7 7 8 7 7 7
7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7
Metadata: {'input': ((7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7), (7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7), (7, 7, 7, 7, 7, 7, 8, 7, 8, 7, 7), (7, 7, 7, 7, 7, 8, 7, 8, 7, 8, 7), (7, 7, 7, 7, 7, 7, 8, 7, 8, 7, 7), (7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7), (7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7), (7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7)), 'output': ((7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7), (7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7), (7, 7, 7, 7, 7, 7, 8, 7, 8, 7, 7), (7, 7, 7, 7, 7, 8, 7, 8, 7, 8, 7), (7, 7, 7, 7, 7, 7, 8, 7, 8, 7, 7), (7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7), (7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7), (7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7)), 'task_id': '11852cab', 'difficulty': {'rng': 0.09651305327452808, 'pso': 0.15228956228956228}}

Example 3:
Question: Find the common rule that maps an input grid to an output grid, given the examples below.

Example 1:

Input:
9 9
9 9
Output:
9 9
9 9
9 9
9 9

Example 2:

Input:
4 4 4 6
Output:
4 4 4 6
4 4 4 6

Example 3:

Input:
4 1 1
4 4 4
Output:
4 1 1
4 4 4
4 4 4
4 1 1


Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Your final answer should just be the text output grid itself.

Input:
1 1 1 1 1
1 1 1 1 1

Answer: 1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
Metadata: {'input': ((1, 1, 1, 1, 1), (1, 1, 1, 1, 1)), 'output': ((1, 1, 1, 1, 1), (1, 1, 1, 1, 1), (1, 1, 1, 1, 1), (1, 1, 1, 1, 1)), 'task_id': '8be77c9e', 'difficulty': {'rng': 0.09322002370336528, 'pso': 0.0638888888888889}}

rectangle_count

Generates RectangleCount Puzzles with configurable parameters

Default configuration:

max_rectangles = 10
width = 80
height = 80
seed = 42
size = 500

Example tasks:

Example 1:
Question: How many rectangles do you see? Single rectangles are outlined with a '#', overlapping rectangles (max 2) are shown with '█'. 

                                                                                 
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                 ##################################################             
                 #                                                #             
                 #                                                #             
                 #                                                #             
                 #                                                #             
                 #                                                #             
                 #                                                #             
                 #                                                #             
                 #                                                #             
                 #                                                #             
                 #                                                #             
                 #                                                #             
                 #                                                #             
                 ##################################################             
                                                                                
                                                                                
                                                                                
                                                                                
   ######################################                                       
   #                                    #                                       
   #                                    #                                       
   #                                    #                                       
   #                                    #                                       
   #                                    #                                       
   #                                    #                                       
   #                                    #                                       
   #                                    #                                       
   #                                    #                                       
   #                                    #                                       
   #                                    #                                       
   #                                    #                                       
   #                                    #                                       
   #                                    #                                       
   #                                    #                                       
   ######################################                                       
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                

Answer: 2

Example 2:
Question: How many rectangles do you see? Single rectangles are outlined with a '#', overlapping rectangles (max 2) are shown with '█'. 

                                                                                 
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                    ############                                
                                    #          #                                
                                    #          #                                
                                    #          #                                
                                    #          #                                
                                    #          #                                
                                    #          #                                
                                    #          #                                
                                    #          #                                
                                    #          #                                
                                    #          #                                
                                    #          #                                
                                    #          #                                
                                    ############                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                

Answer: 1

Example 3:
Question: How many rectangles do you see? Single rectangles are outlined with a '#', overlapping rectangles (max 2) are shown with '█'. 

                                                                                 
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                         #########################              
                                         #                       #              
                                         #                       #              
                                         #                       #              
                                         #                       #              
                                         #                       ############   
                                         #                       ##         #   
                                         #                       ##         #   
                                         #                       ##         #   
                                         #                       ##         #   
                                         #                       ##         #   
                                    #####█#######################██#########█#  
                                    #    #                       ##         ##  
                                    #    #                       ##         ##  
                                    #    #                       ##         ##  
                                    #    #                       ##         ##  
                                    #    #                       ##         ##  
                                    #    #                       ##         ##  
                                    #    #                       ##         ##  
                                    #    #                       ##         ##  
                                    #####█#######################██#########█#  
                                         #                       ##         #   
                                         #                       ##         #   
                                         #                       ##         #   
                                         #                       ##         #   
                                         #                       ##         #   
                                         #                       ##         #   
                                         #                       ##         #   
                                         #      ##########       ##         #   
                                         #      #        #       ############   
                                         #      #        #       #              
                                         #      ##########       #              
                                         #                       #              
                                         #                       #              
                                         #                       #              
                                         #                       #              
                                         #                       #              
                                         #                       #              
                                         #                       #              
                                         #                       #              
                                         #                       #              
                                         #                       #              
                                         #                       #              
                                         #                       #              
                                         #                       #              
                                         #########################              
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
                                                                                
            #######################                                             
            #                     #                                             
            #                     #                                             
            #                     #                                             
            #                     #                                             
            #                     #                                             
            #                     #                                             
            #               ######█###                                          
            #               #     #  #                                          
            #               ######█###                                          
            #                     #   ###########################               
            #                     #   #                         #               
            #                     #   #                         #               
            #######################   ###########################               
                                                                                

Answer: 7

rotate_matrix

Generates Rotate Matrix exercises with configurable difficulty

Default configuration:

max_n = 10
max_rotations = 4
size = 500
seed = 42

Example tasks:

Example 1:
Question: Given a square matrix, your job is to rotate it clockwise.

Example:

Input: Rotate the matrix below by 90 degrees clockwise:
1 2 3
4 5 6
7 8 9

Output:
7 4 1
8 5 2
9 6 3

Rotate the matrix below by 90 degrees clockwise:
3 1
2 0

Answer: 2 3
0 1
Metadata: {'matrix': [[3, 1], [2, 0]], 'num_rotations': 1, 'solution': [[2, 3], [0, 1]]}

Example 2:
Question: Given a square matrix, your job is to rotate it clockwise.

Example:

Input: Rotate the matrix below by 90 degrees clockwise:
1 2 3
4 5 6
7 8 9

Output:
7 4 1
8 5 2
9 6 3

Rotate the matrix below by 180 degrees clockwise:
0

Answer: 0
Metadata: {'matrix': [[0]], 'num_rotations': 2, 'solution': [[0]]}

Example 3:
Question: Given a square matrix, your job is to rotate it clockwise.

Example:

Input: Rotate the matrix below by 90 degrees clockwise:
1 2 3
4 5 6
7 8 9

Output:
7 4 1
8 5 2
9 6 3

Rotate the matrix below by 180 degrees clockwise:
28 17 38 29 8 15 26
35 13 37 39 27 40 20
4 30 23 16 3 5 48
9 25 2 46 47 21 22
31 12 41 43 19 32 10
6 0 36 45 42 1 18
14 24 11 7 44 34 33

Answer: 33 34 44 7 11 24 14
18 1 42 45 36 0 6
10 32 19 43 41 12 31
22 21 47 46 2 25 9
48 5 3 16 23 30 4
20 40 27 39 37 13 35
26 15 8 29 38 17 28
Metadata: {'matrix': [[28, 17, 38, 29, 8, 15, 26], [35, 13, 37, 39, 27, 40, 20], [4, 30, 23, 16, 3, 5, 48], [9, 25, 2, 46, 47, 21, 22], [31, 12, 41, 43, 19, 32, 10], [6, 0, 36, 45, 42, 1, 18], [14, 24, 11, 7, 44, 34, 33]], 'num_rotations': 2, 'solution': [[33, 34, 44, 7, 11, 24, 14], [18, 1, 42, 45, 36, 0, 6], [10, 32, 19, 43, 41, 12, 31], [22, 21, 47, 46, 2, 25, 9], [48, 5, 3, 16, 23, 30, 4], [20, 40, 27, 39, 37, 13, 35], [26, 15, 8, 29, 38, 17, 28]]}

rubiks_cube

Generates RubiksCube tasks

Default configuration:

scramble_steps = 3
cube_size = 3
remove_ansi = True
seed = 42
size = 500

Example tasks:

Example 1:
Question: You are given a 3x3x3 Rubik's cube. It looks like this:

          G  Y  G                   
          G  Y  G                   
          G  R  G                   
 W  W  W  O  G  O  Y  Y  Y  R  B  R 
 R  R  R  W  G  W  O  O  O  Y  B  Y 
 R  R  R  W  G  W  O  O  O  Y  B  Y 
          B  O  B                   
          B  W  B                   
          B  W  B                   
 

Please provide a solution to solve this cube using Singmaster notation.
Answer: None
Metadata: {'cube_size': 3, 'scramble_steps': 3, 'scramble_moves': "F L' R", 'example_correct_answer': "L F' U' R D B' D' U R U' R' U B U' B' U' R' U R U B U' B' U R' U R U B U' B' U' B' U B U L U' L' U' B' U B U L U' L' U B' U B U L U' L' F R U R' U' F' U' R U R' U R U U R' F U' B' U F' U' B R' D' R D R' D' R D R' D' R D R' D' R D U R' D' R D R' D' R D U R' D' R D R' D' R D R' D' R D R' D' R D U R' D' R D R' D' R D U"}

Example 2:
Question: You are given a 3x3x3 Rubik's cube. It looks like this:

          Y  Y  R                   
          Y  Y  R                   
          G  G  R                   
 B  B  Y  R  R  B  W  W  W  G  O  O 
 R  R  W  G  G  G  Y  O  O  B  B  Y 
 R  R  W  G  G  G  Y  O  O  B  B  Y 
          O  O  O                   
          B  W  W                   
          B  W  W                   
 

Please provide a solution to solve this cube using Singmaster notation.
Answer: None
Metadata: {'cube_size': 3, 'scramble_steps': 3, 'scramble_moves': "L' F U'", 'example_correct_answer': "U' D' B D L' U' F D R' D' U' R U' R' F' U U F U F U' F' U' L' U L U F U' F' U L' U L U F U' F' R U' R' U' F' U F R' U R U B U' B' U' U' B' U B U L U' L' F R U R' U' R U R' U' F' U R U R' U R U U R' U' R U R' U R U U R' U' R U' L' U R' U' L U F U' B' U F' U' B R' D' R D R' D' R D U U R' D' R D R' D' R D U R' D' R D R' D' R D U"}

Example 3:
Question: You are given a 3x3x3 Rubik's cube. It looks like this:

          Y  Y  W                   
          Y  Y  W                   
          Y  Y  W                   
 G  G  G  O  O  B  O  O  O  G  R  R 
 R  R  R  G  G  B  O  O  O  G  B  B 
 R  R  R  G  G  R  B  B  B  O  B  B 
          W  W  Y                   
          W  W  Y                   
          W  W  Y                   
 

Please provide a solution to solve this cube using Singmaster notation.
Answer: None
Metadata: {'cube_size': 3, 'scramble_steps': 3, 'scramble_moves': "U R' R'", 'example_correct_answer': "R R U'"}

self_reference

Generates self-referential puzzles

Default configuration:

difficulty = 5
seed = 42
size = 500

Example tasks:

Example 1:
Question: Given the truthfulness of these statements, please tell me the number of possible solutions: 
 - Statement 1: 'At least 1 of these 7 statements are true.'
 - Statement 2: 'At most 3 of these 7 statements are false.'
 - Statement 3: 'Exactly 4 of these 7 statements are true.'
 - Statement 4: 'Exactly 3 of these 7 statements are false.'
 - Statement 5: 'Either Statement 3 or Statement 4 is true, but not both.'
 - Statement 6: 'The number of true statements is a prime number.'
 - Statement 7: 'The number of false statements is a composite number.'

Answer: 4

Example 2:
Question: Given the truthfulness of these statements, please tell me the number of possible solutions: 
 - Statement 1: 'At least 4 of these 7 statements are true.'
 - Statement 2: 'At most 5 of these 7 statements are false.'
 - Statement 3: 'Exactly 7 of these 7 statements are true.'
 - Statement 4: 'Exactly 1 of these 7 statements are false.'
 - Statement 5: 'Either Statement 3 or Statement 4 is true, but not both.'
 - Statement 6: 'The number of true statements is a prime number.'
 - Statement 7: 'The number of false statements is a composite number.'

Answer: 4

Example 3:
Question: Given the truthfulness of these statements, please tell me the number of possible solutions: 
 - Statement 1: 'At least 2 of these 7 statements are true.'
 - Statement 2: 'At most 5 of these 7 statements are false.'
 - Statement 3: 'Exactly 0 of these 7 statements are true.'
 - Statement 4: 'Exactly 3 of these 7 statements are false.'
 - Statement 5: 'Either Statement 3 or Statement 4 is true, but not both.'
 - Statement 6: 'The number of true statements is a prime number.'
 - Statement 7: 'The number of false statements is a composite number.'

Answer: 2

sentence_reordering

Generates sentence reordering tasks from text spans

Default configuration:

min_words_in_sentence = 3
max_words_in_sentence = 20
seed = 42
size = 500

Example tasks:

Example 1:
Question: Restore the correct order of words in the following sentence: wish could get I sleep. "I some
Answer: "I wish I could get some sleep.
Metadata: {'word_count': 7}

Example 2:
Question: Restore the correct order of words in the following sentence: the high level name. itself its unable it maintain at was of to Unfortunately,
Answer: Unfortunately, it was unable to maintain itself at the high level of its name.
Metadata: {'word_count': 14}

Example 3:
Question: Restore the correct order of words in the following sentence: developed by For the unutilized. energy falls ages went the
Answer: For ages the the energy developed by falls went unutilized.
Metadata: {'word_count': 10}

simple_equations

Generates simple equations with one variable to solve

Default configuration:

min_terms = 2
max_terms = 4
min_value = 1
max_value = 100
operators = ('+', '-', '*')
seed = 42
size = 500

Example tasks:

Example 1:
Question: Determine the value of u that satisfies: 32*u + 4 = 580
Answer: 18
Metadata: {'equation': '32*u + 4 = 580', 'variable': 'u'}

Example 2:
Question: Solve for b: 82080*b = 1067040
Answer: 13
Metadata: {'equation': '82080*b = 1067040', 'variable': 'b'}

Example 3:
Question: Determine the value of n that satisfies: 29*n - 5 = 430
Answer: 15
Metadata: {'equation': '29*n - 5 = 430', 'variable': 'n'}

simple_geometry

A dataset for simple polygon angle-finding tasks. We randomly choose the number of sides N within [min_sides, max_sides]. We then generate (N-1) random angles (in degrees), ensuring their sum is strictly less than the total sum for an (N)-sided convex polygon (which is 180*(N-2)). The question asks for the missing angle; the answer is computed by subtracting the sum of known angles from 180*(N-2).

Default configuration:

min_sides = 3
max_sides = 6
min_angle = 10
max_angle = 170
seed = 42
size = 100

Example tasks:

Example 1:
Question: Given a convex polygon with 3 sides, its first 2 interior angles are: 16.0°, 80.0°. What is the measure of the remaining interior angle (in degrees)?
Answer: 84
Metadata: {'n_sides': 3, 'known_angles': [16.0, 80.0], 'sum_of_known_angles': 96.0, 'missing_angle_raw': 84.0, 'missing_angle_rounded': 84, 'total_interior_sum': 180}

Example 2:
Question: A convex polygon has 3 sides. The measures of the first 2 interior angles are: 83.0°, 46.0°. Find the measure of the last interior angle.
Answer: 51
Metadata: {'n_sides': 3, 'known_angles': [83.0, 46.0], 'sum_of_known_angles': 129.0, 'missing_angle_raw': 51.0, 'missing_angle_rounded': 51, 'total_interior_sum': 180}

Example 3:
Question: Given a convex polygon with 6 sides, its first 5 interior angles are: 143.0°, 148.0°, 39.0°, 55.0°, 107.0°. What is the measure of the remaining interior angle (in degrees)?
Answer: 228
Metadata: {'n_sides': 6, 'known_angles': [143.0, 148.0, 39.0, 55.0, 107.0], 'sum_of_known_angles': 492.0, 'missing_angle_raw': 228.0, 'missing_angle_rounded': 228, 'total_interior_sum': 720}

simple_integration

Generates simple integration problems with one variable

Default configuration:

min_terms = 2
max_terms = 5
min_degree = 1
max_degree = 10
min_bounds = 1
max_bounds = 10
operators = ('+', '-')
symbols = ('x', 'X')
seed = 42
size = 500

Example tasks:

Example 1:
Question: Find the indefinite integral: ∫ 70*x**6 + 12*x**2/5 dx
In addition, When doing calculation, Use the following instructions together with your mathematical ingenuity to solve the integral problems
## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
## 2. Always use * when doing all sorts of multiplcation in your reasoning steps. For example Use [-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C] instead of [-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C].

Answer: 10*x**7 + 4*x**3/5 + C
Metadata: {'integrand': '70*x**6 + 12*x**2/5', 'variable': 'x', 'expected_answer_expression': 10*x**7 + 4*x**3/5}

Example 2:
Question: Find the indefinite integral: ∫ 49*x**6/10 + 48*x**5 - 4*x - 10/9 dx
In addition, When doing calculation, Use the following instructions together with your mathematical ingenuity to solve the integral problems
## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
## 2. Always use * when doing all sorts of multiplcation in your reasoning steps. For example Use [-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C] instead of [-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C].

Answer: 7*x**7/10 + 8*x**6 - 2*x**2 - 10*x/9 + C
Metadata: {'integrand': '49*x**6/10 + 48*x**5 - 4*x - 10/9', 'variable': 'x', 'expected_answer_expression': 7*x**7/10 + 8*x**6 - 2*x**2 - 10*x/9}

Example 3:
Question: Find the indefinite integral: ∫ -28*X**3 + 8*X dx
In addition, When doing calculation, Use the following instructions together with your mathematical ingenuity to solve the integral problems
## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
## 2. Always use * when doing all sorts of multiplcation in your reasoning steps. For example Use [-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C] instead of [-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C].

Answer: -7*X**4 + 4*X**2 + C
Metadata: {'integrand': '-28*X**3 + 8*X', 'variable': 'X', 'expected_answer_expression': -7*X**4 + 4*X**2}

sokoban

Generates Sokoban games with configurable parameters

Default configuration:

min_w = 6
min_h = 6
max_w = 10
max_h = 10
min_boxes = 6
max_boxes = 10
seed = 42
size = 500

Example tasks:

Example 1:
Question: You are going to solve a 'sokoban' puzzle.

* - The player
% - The player on a goal
@ - A box
X - A goal
$ - A box on a goal
+ - A wall
- - An empty position

Your solution must be a string of characters, ex: LDURRUDL.

Here is your puzzle:
+ + + + + + + + +  
+ + X - @ * @ X +  
+ + + - - @ - + +  
+ + + - - - X $ +  
+ + + + - + + + +  
+ + $ + + + + + +  
+ + + + + + + + +  


Answer: RLDULLRRDLDR
Metadata: {'gamestr': '+ + + + + + + + +  \n+ + X - @ * @ X +  \n+ + + - - @ - + +  \n+ + + - - - X $ +  \n+ + + + - + + + +  \n+ + $ + + + + + +  \n+ + + + + + + + +  \n\n', 'difficulty': {'size': (7, 9), 'num_steps': 12}}

Example 2:
Question: You are going to solve a 'sokoban' puzzle.

* - The player
% - The player on a goal
@ - A box
X - A goal
$ - A box on a goal
+ - A wall
- - An empty position

Your solution must be a string of characters, ex: LDURRUDL.

Here is your puzzle:
+ + + + + +  
+ - * - - +  
+ @ - - @ +  
+ X - @ - +  
+ - - - X +  
+ X - @ X +  
+ - - - - +  
+ + + + + +  


Answer: LDRRDRDDLLURURDULUURDD
Metadata: {'gamestr': '+ + + + + +  \n+ - * - - +  \n+ @ - - @ +  \n+ X - @ - +  \n+ - - - X +  \n+ X - @ X +  \n+ - - - - +  \n+ + + + + +  \n\n', 'difficulty': {'size': (8, 6), 'num_steps': 22}}

Example 3:
Question: You are going to solve a 'sokoban' puzzle.

* - The player
% - The player on a goal
@ - A box
X - A goal
$ - A box on a goal
+ - A wall
- - An empty position

Your solution must be a string of characters, ex: LDURRUDL.

Here is your puzzle:
+ + + + + + + + + + + +  
+ - $ - X + - - - - - +  
+ - @ - - - - - @ - X +  
+ - * - @ - - X - $ - +  
+ - - - - X + - - - - +  
+ + - - - - + $ - @ - +  
+ + + - - - - - - - - +  
+ + + - - - $ - - - - +  
+ + + + - - - - - - - +  
+ + + + + + + + + + + +  


Answer: RRRRURRRLDDRRDLULDRDLLLLULLDRDRUULUUULDLLURRDRU
Metadata: {'gamestr': '+ + + + + + + + + + + +  \n+ - $ - X + - - - - - +  \n+ - @ - - - - - @ - X +  \n+ - * - @ - - X - $ - +  \n+ - - - - X + - - - - +  \n+ + - - - - + $ - @ - +  \n+ + + - - - - - - - - +  \n+ + + - - - $ - - - - +  \n+ + + + - - - - - - - +  \n+ + + + + + + + + + + +  \n\n', 'difficulty': {'size': (10, 12), 'num_steps': 47}}

spell_backward

Generates tasks to spell words backward

Default configuration:

min_word_len = 3
seed = 42
size = 500

Example tasks:

Example 1:
Question: Spell this word backward (example: sun -> nus): Project
Answer: tcejorP
Metadata: {'word': 'Project', 'word_len': 7}

Example 2:
Question: Spell this word backward (example: sun -> nus): Would
Answer: dluoW
Metadata: {'word': 'Would', 'word_len': 5}

Example 3:
Question: Spell this word backward (example: sun -> nus): One
Answer: enO
Metadata: {'word': 'One', 'word_len': 3}

spiral_matrix

Generates Spiral Matrix exercises with configurable difficulty

Default configuration:

max_n = 10
size = 500
seed = 42

Example tasks:

Example 1:
Question: Given a matrix, your job is to generate a list of elements in spiral order, starting from the top-left element.

Example:

Input:
1 2 3
4 5 6
7 8 9

Output: 1 2 3 6 9 8 7 4 5

For the matrix below, what is the list of elements in spiral order?
3 0
3 4

Answer: 3 0 4 3
Metadata: {'matrix': [[3, 0], [3, 4]], 'solution': [3, 0, 4, 3]}

Example 2:
Question: Given a matrix, your job is to generate a list of elements in spiral order, starting from the top-left element.

Example:

Input:
1 2 3
4 5 6
7 8 9

Output: 1 2 3 6 9 8 7 4 5

For the matrix below, what is the list of elements in spiral order?
4

Answer: 4
Metadata: {'matrix': [[4]], 'solution': [4]}

Example 3:
Question: Given a matrix, your job is to generate a list of elements in spiral order, starting from the top-left element.

Example:

Input:
1 2 3
4 5 6
7 8 9

Output: 1 2 3 6 9 8 7 4 5

For the matrix below, what is the list of elements in spiral order?
6 4 1 8 2 6 2
9 5 1 3 4 8 0
1 2 1 4 0 5 2
9 5 5 9 6 1 0
8 3 3 0 5 7 0
8 1 4 6 9 7 1
4 1 3 4 6 1 3

Answer: 6 4 1 8 2 6 2 0 2 0 0 1 3 1 6 4 3 1 4 8 8 9 1 9 5 1 3 4 8 5 1 7 7 9 6 4 1 3 5 2 1 4 0 6 5 0 3 5 9
Metadata: {'matrix': [[6, 4, 1, 8, 2, 6, 2], [9, 5, 1, 3, 4, 8, 0], [1, 2, 1, 4, 0, 5, 2], [9, 5, 5, 9, 6, 1, 0], [8, 3, 3, 0, 5, 7, 0], [8, 1, 4, 6, 9, 7, 1], [4, 1, 3, 4, 6, 1, 3]], 'solution': [6, 4, 1, 8, 2, 6, 2, 0, 2, 0, 0, 1, 3, 1, 6, 4, 3, 1, 4, 8, 8, 9, 1, 9, 5, 1, 3, 4, 8, 5, 1, 7, 7, 9, 6, 4, 1, 3, 5, 2, 1, 4, 0, 6, 5, 0, 3, 5, 9]}

string_insertion

Generates String Insertion exercises with configurable difficulty

Default configuration:

min_string_length = 5
max_string_length = 20
size = 500
seed = 42

Example tasks:

Example 1:
Question: Given a string consisting of characters A, B, C, D, and E, your job is to insert a character according to the following pattern:
1. If there is a substring ABCD in the string, insert the character A after the substring.
2. If there is a substring BCDE in the string, insert the character B after the substring.
3. If there is a substring CDEA in the string, insert the character C after the substring.
4. If there is a substring DEAB in the string, insert the character D after the substring.
5. If there is a substring EABC in the string, insert the character E after the substring.

Once you have inserted a character, you have to skip over the substring and the inserted character and continue the search from the next character.

Example
- Input: DDABCDEEDEAB
- Output: DDABCDAEEDEABD
- Explanation:
    - Theere are two inserted characters: DDABCD[A]EEDEAB[D] (shown in square brackets)
    - First, we insert A after ABCD.
    - Even though with the newly inserted 'A' we can obtain the substring BCD[A], we can't use it to insert another character.
    - Lastly, we insert D after DEAB.

Given the following string, provide the answer after inserting the characters according to the pattern: ['A', 'C', 'B', 'B', 'B', 'A', 'E', 'A']

Answer: ACBBBAEA
Metadata: {'string': ['A', 'C', 'B', 'B', 'B', 'A', 'E', 'A'], 'solution': 'ACBBBAEA'}

Example 2:
Question: Given a string consisting of characters A, B, C, D, and E, your job is to insert a character according to the following pattern:
1. If there is a substring ABCD in the string, insert the character A after the substring.
2. If there is a substring BCDE in the string, insert the character B after the substring.
3. If there is a substring CDEA in the string, insert the character C after the substring.
4. If there is a substring DEAB in the string, insert the character D after the substring.
5. If there is a substring EABC in the string, insert the character E after the substring.

Once you have inserted a character, you have to skip over the substring and the inserted character and continue the search from the next character.

Example
- Input: DDABCDEEDEAB
- Output: DDABCDAEEDEABD
- Explanation:
    - Theere are two inserted characters: DDABCD[A]EEDEAB[D] (shown in square brackets)
    - First, we insert A after ABCD.
    - Even though with the newly inserted 'A' we can obtain the substring BCD[A], we can't use it to insert another character.
    - Lastly, we insert D after DEAB.

Given the following string, provide the answer after inserting the characters according to the pattern: ['C', 'B', 'D', 'C', 'A', 'D']

Answer: CBDCAD
Metadata: {'string': ['C', 'B', 'D', 'C', 'A', 'D'], 'solution': 'CBDCAD'}

Example 3:
Question: Given a string consisting of characters A, B, C, D, and E, your job is to insert a character according to the following pattern:
1. If there is a substring ABCD in the string, insert the character A after the substring.
2. If there is a substring BCDE in the string, insert the character B after the substring.
3. If there is a substring CDEA in the string, insert the character C after the substring.
4. If there is a substring DEAB in the string, insert the character D after the substring.
5. If there is a substring EABC in the string, insert the character E after the substring.

Once you have inserted a character, you have to skip over the substring and the inserted character and continue the search from the next character.

Example
- Input: DDABCDEEDEAB
- Output: DDABCDAEEDEABD
- Explanation:
    - Theere are two inserted characters: DDABCD[A]EEDEAB[D] (shown in square brackets)
    - First, we insert A after ABCD.
    - Even though with the newly inserted 'A' we can obtain the substring BCD[A], we can't use it to insert another character.
    - Lastly, we insert D after DEAB.

Given the following string, provide the answer after inserting the characters according to the pattern: ['E', 'E', 'A', 'B', 'D', 'B', 'C', 'A', 'B', 'A', 'E', 'A', 'A', 'B', 'E', 'C', 'D', 'E']

Answer: EEABDBCABAEAABECDE
Metadata: {'string': ['E', 'E', 'A', 'B', 'D', 'B', 'C', 'A', 'B', 'A', 'E', 'A', 'A', 'B', 'E', 'C', 'D', 'E'], 'solution': 'EEABDBCABAEAABECDE'}

string_manipulation

Generates String Insertion exercises with configurable difficulty

Default configuration:

min_string_length = 5
max_string_length = 20
min_num_rules = 3
max_num_rules = 8
size = 500
seed = 42

Example tasks:

Example 1:
Question: Your job is to repeatedly transform a string according to a set of rules until no further transformations can be performed, or a state is repeated.

Evaluate the following rules in order, and apply the first applicable rule to the string:
1. If the string contains an even number of 'b's (and at least one 'b'), append 'ab' at the end.
2. If the string prefix is 'bc', delete the first two characters and append 'aa' to the end.
3. If the string ends with 'ca', remove the last character.
4. If the string suffix is 'ac', replace it with 'cb'.
5. If the string prefix is 'ab', replace it with 'ca'.
6. If the string contains 'ca' (not at the start), remove the first occurrence found after the first character.
7. If the string suffix is 'bb', delete the last two characters.
8. If the string starts with 'ac', replace the first two characters with 'zz'.

Once you have applied a rule, repeat the process with the new string until no further transformations can be performed (i.e. the string doesn't change), or a state is repeated.
If a state is repeated, the process is terminated, and the repeated state is discarded (i.e. is not considered as the final answer) and the state before the repeated state is considered as the final answer.

Example:
- Input:
    - String: abbac
    - Rules:
        1. If the string prefix is 'ab', replace it with 'ca'.
        2. If the string prefix is 'ca', replace it with 'bb' and append 'c' to the end.
        3. If the string ends with 'aa', replace it with 'cc'.
- Output: bbbacc
- Explanation:
    - In the first iteration, rule 1 is applied to the string abbac, resulting in cabac
    - In the second interation, rule 1 doesn't apply, but rule 2 is applied to the string cabac, resulting in bbbacc
    - In the third iteration, none of the rules (1, 2, 3) apply, so the process is terminated, and the final answer is bbbacc

Transform the following string according to the above list of rules:
acbaaaca

Answer: zzbaacbab
Metadata: {'string': 'acbaaaca', 'solution': 'zzbaacbab', 'states': ['acbaaaca', 'acbaaac', 'acbaacb', 'acbaacbab', 'zzbaacbab'], 'selected_rules': ["If the string contains an even number of 'b's (and at least one 'b'), append 'ab' at the end.", "If the string prefix is 'bc', delete the first two characters and append 'aa' to the end.", "If the string ends with 'ca', remove the last character.", "If the string suffix is 'ac', replace it with 'cb'.", "If the string prefix is 'ab', replace it with 'ca'.", "If the string contains 'ca' (not at the start), remove the first occurrence found after the first character.", "If the string suffix is 'bb', delete the last two characters.", "If the string starts with 'ac', replace the first two characters with 'zz'."]}

Example 2:
Question: Your job is to repeatedly transform a string according to a set of rules until no further transformations can be performed, or a state is repeated.

Evaluate the following rules in order, and apply the first applicable rule to the string:
1. If the string suffix is 'bb', delete the last two characters.
2. If the string starts with 'bb', remove the second character.
3. If the string ends with 'aa', replace it with 'cc'.
4. If the string prefix is 'ab', replace it with 'ca'.
5. If the string ends with 'ca', remove the last character.
6. If the string contains 'bca', delete the first occurrence entirely.
7. If the string prefix is 'ca', replace it with 'bb' and append 'c' to the end.
8. If the string length is greater than 15, remove the middle character.

Once you have applied a rule, repeat the process with the new string until no further transformations can be performed (i.e. the string doesn't change), or a state is repeated.
If a state is repeated, the process is terminated, and the repeated state is discarded (i.e. is not considered as the final answer) and the state before the repeated state is considered as the final answer.

Example:
- Input:
    - String: abbac
    - Rules:
        1. If the string prefix is 'ab', replace it with 'ca'.
        2. If the string prefix is 'ca', replace it with 'bb' and append 'c' to the end.
        3. If the string ends with 'aa', replace it with 'cc'.
- Output: bbbacc
- Explanation:
    - In the first iteration, rule 1 is applied to the string abbac, resulting in cabac
    - In the second interation, rule 1 doesn't apply, but rule 2 is applied to the string cabac, resulting in bbbacc
    - In the third iteration, none of the rules (1, 2, 3) apply, so the process is terminated, and the final answer is bbbacc

Transform the following string according to the above list of rules:
bcabbc

Answer: bc
Metadata: {'string': 'bcabbc', 'solution': 'bc', 'states': ['bcabbc', 'bbc', 'bc'], 'selected_rules': ["If the string suffix is 'bb', delete the last two characters.", "If the string starts with 'bb', remove the second character.", "If the string ends with 'aa', replace it with 'cc'.", "If the string prefix is 'ab', replace it with 'ca'.", "If the string ends with 'ca', remove the last character.", "If the string contains 'bca', delete the first occurrence entirely.", "If the string prefix is 'ca', replace it with 'bb' and append 'c' to the end.", 'If the string length is greater than 15, remove the middle character.']}

Example 3:
Question: Your job is to repeatedly transform a string according to a set of rules until no further transformations can be performed, or a state is repeated.

Evaluate the following rules in order, and apply the first applicable rule to the string:
1. If the string contains 'acb', replace the first occurrence with its reverse ('bca').
2. If the string length is greater than 15, remove the middle character.
3. If the string starts with 'ac', replace the first two characters with 'zz'.
4. If the string ends with 'ba', replace it with 'ab'.
5. If the string starts with 'cc', remove the first two characters.
6. If the string suffix is 'ac', replace it with 'cb'.
7. If the string prefix is 'ca', replace it with 'bb' and append 'c' to the end.
8. If the string prefix is 'cb', replace it with 'aa' and delete the last character.

Once you have applied a rule, repeat the process with the new string until no further transformations can be performed (i.e. the string doesn't change), or a state is repeated.
If a state is repeated, the process is terminated, and the repeated state is discarded (i.e. is not considered as the final answer) and the state before the repeated state is considered as the final answer.

Example:
- Input:
    - String: abbac
    - Rules:
        1. If the string prefix is 'ab', replace it with 'ca'.
        2. If the string prefix is 'ca', replace it with 'bb' and append 'c' to the end.
        3. If the string ends with 'aa', replace it with 'cc'.
- Output: bbbacc
- Explanation:
    - In the first iteration, rule 1 is applied to the string abbac, resulting in cabac
    - In the second interation, rule 1 doesn't apply, but rule 2 is applied to the string cabac, resulting in bbbacc
    - In the third iteration, none of the rules (1, 2, 3) apply, so the process is terminated, and the final answer is bbbacc

Transform the following string according to the above list of rules:
cccaababaaacaaaccb

Answer: bbababcaaaccbc
Metadata: {'string': 'cccaababaaacaaaccb', 'solution': 'bbababcaaaccbc', 'states': ['cccaababaaacaaaccb', 'cccaababaacaaaccb', 'cccaababacaaaccb', 'cccaababcaaaccb', 'caababcaaaccb', 'bbababcaaaccbc'], 'selected_rules': ["If the string contains 'acb', replace the first occurrence with its reverse ('bca').", 'If the string length is greater than 15, remove the middle character.', "If the string starts with 'ac', replace the first two characters with 'zz'.", "If the string ends with 'ba', replace it with 'ab'.", "If the string starts with 'cc', remove the first two characters.", "If the string suffix is 'ac', replace it with 'cb'.", "If the string prefix is 'ca', replace it with 'bb' and append 'c' to the end.", "If the string prefix is 'cb', replace it with 'aa' and delete the last character."]}

string_synthesis

Generates String Synthesis exercises with configurable difficulty

Default configuration:

min_initial_blocks = 0
max_initial_blocks = 5
max_iterations = 1000
size = 500
seed = 42

Example tasks:

Example 1:
Question: There are nine different blocks [A] [B] [C] {A} {B} {C} (A) (B) (C)
1. One [A], one [B], and one [C] can be combined to form one {A}.
2. One [A] and one [B] can be combined to form one {C}.
3. One [B] and one [C] can be combined to form one {B}.
4. Two [C] can be combined to form one {C}.
5. One {A} and one {C} can be combined to form one (A) and one (B).
6. Two {B} can be combined to form one (C).

Given a certain number of initial blocks, your job is to cycle through the rules 1-6 above, synthesizing new blocks until no more rules can be applied, or until a state (counts of each block type) is repeated.
In the case a state is repeated the answer is the state before the repetition!

The output should be the count of each block type after the rules have been applied in the order they are listed above.
For example 1 0 3 0 2 0 0 0 1 means that you have 1 [A] 0 [B] 3 [C] 0 {A} 2 {B} 0 {C} 0 (A) 0 (B) 1 (C).

Example:
- Input: You have 2 [A], 3 [B], and 3 [C].
- Output: 0 0 0 2 1 0 0 0 0
- Explanation:
    0. Initial state: 2 3 3 0 0 0 0 0 0
    1. We can apply Rule 1 and obtain 1 {A}. New state: 1 2 2 1 0 0 0 0 0
    2. We can apply Rule 1 again and obtain 1 {A}. New state 0 1 1 2 0 0 0 0 0
    3. We can apply Rule 3 and obtain 1 {B}. New state 0 0 0 2 1 0 0 0 0
    4. No more rules can be applied. The answer is 0 0 0 2 1 0 0 0 0

Now, you have 5 [A], 0 [B], and 0 [C] blocks. Provide the count of each block type after applying the above rules.

Answer: 5 0 0 0 0 0 0 0 0
Metadata: {'states': [[5, 0, 0, 0, 0, 0, 0, 0, 0]], 'solution': [5, 0, 0, 0, 0, 0, 0, 0, 0]}

Example 2:
Question: There are nine different blocks [A] [B] [C] {A} {B} {C} (A) (B) (C)
1. One [A], one [B], and one [C] can be combined to form one {A}.
2. One [A] and one [B] can be combined to form one {C}.
3. One [B] and one [C] can be combined to form one {B}.
4. Two [C] can be combined to form one {C}.
5. One {A} and one {C} can be combined to form one (A) and one (B).
6. Two {B} can be combined to form one (C).

Given a certain number of initial blocks, your job is to cycle through the rules 1-6 above, synthesizing new blocks until no more rules can be applied, or until a state (counts of each block type) is repeated.
In the case a state is repeated the answer is the state before the repetition!

The output should be the count of each block type after the rules have been applied in the order they are listed above.
For example 1 0 3 0 2 0 0 0 1 means that you have 1 [A] 0 [B] 3 [C] 0 {A} 2 {B} 0 {C} 0 (A) 0 (B) 1 (C).

Example:
- Input: You have 2 [A], 3 [B], and 3 [C].
- Output: 0 0 0 2 1 0 0 0 0
- Explanation:
    0. Initial state: 2 3 3 0 0 0 0 0 0
    1. We can apply Rule 1 and obtain 1 {A}. New state: 1 2 2 1 0 0 0 0 0
    2. We can apply Rule 1 again and obtain 1 {A}. New state 0 1 1 2 0 0 0 0 0
    3. We can apply Rule 3 and obtain 1 {B}. New state 0 0 0 2 1 0 0 0 0
    4. No more rules can be applied. The answer is 0 0 0 2 1 0 0 0 0

Now, you have 0 [A], 2 [B], and 5 [C] blocks. Provide the count of each block type after applying the above rules.

Answer: 0 0 1 0 0 1 0 0 1
Metadata: {'states': [[0, 2, 5, 0, 0, 0, 0, 0, 0], [0, 1, 4, 0, 1, 0, 0, 0, 0], [0, 0, 3, 0, 2, 0, 0, 0, 0], [0, 0, 1, 0, 2, 1, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 1]], 'solution': [0, 0, 1, 0, 0, 1, 0, 0, 1]}

Example 3:
Question: There are nine different blocks [A] [B] [C] {A} {B} {C} (A) (B) (C)
1. One [A], one [B], and one [C] can be combined to form one {A}.
2. One [A] and one [B] can be combined to form one {C}.
3. One [B] and one [C] can be combined to form one {B}.
4. Two [C] can be combined to form one {C}.
5. One {A} and one {C} can be combined to form one (A) and one (B).
6. Two {B} can be combined to form one (C).

Given a certain number of initial blocks, your job is to cycle through the rules 1-6 above, synthesizing new blocks until no more rules can be applied, or until a state (counts of each block type) is repeated.
In the case a state is repeated the answer is the state before the repetition!

The output should be the count of each block type after the rules have been applied in the order they are listed above.
For example 1 0 3 0 2 0 0 0 1 means that you have 1 [A] 0 [B] 3 [C] 0 {A} 2 {B} 0 {C} 0 (A) 0 (B) 1 (C).

Example:
- Input: You have 2 [A], 3 [B], and 3 [C].
- Output: 0 0 0 2 1 0 0 0 0
- Explanation:
    0. Initial state: 2 3 3 0 0 0 0 0 0
    1. We can apply Rule 1 and obtain 1 {A}. New state: 1 2 2 1 0 0 0 0 0
    2. We can apply Rule 1 again and obtain 1 {A}. New state 0 1 1 2 0 0 0 0 0
    3. We can apply Rule 3 and obtain 1 {B}. New state 0 0 0 2 1 0 0 0 0
    4. No more rules can be applied. The answer is 0 0 0 2 1 0 0 0 0

Now, you have 3 [A], 4 [B], and 4 [C] blocks. Provide the count of each block type after applying the above rules.

Answer: 0 0 0 3 1 0 0 0 0
Metadata: {'states': [[3, 4, 4, 0, 0, 0, 0, 0, 0], [2, 3, 3, 1, 0, 0, 0, 0, 0], [1, 2, 2, 2, 0, 0, 0, 0, 0], [0, 1, 1, 3, 0, 0, 0, 0, 0], [0, 0, 0, 3, 1, 0, 0, 0, 0]], 'solution': [0, 0, 0, 3, 1, 0, 0, 0, 0]}

sudoku

Generates sudoku puzzles with configurable difficulty

Default configuration:

min_empty = 30
max_empty = 50
seed = 42
size = 500

Example tasks:

Example 1:
Question: Solve this Sudoku puzzle:
4 _ _ _ 5 2 _ 3 _
_ _ 3 4 6 _ _ _ _
6 1 2 _ _ 8 4 _ _
1 _ _ _ _ _ 7 9 5
3 _ _ 7 1 _ _ 2 6
7 _ _ 5 _ _ _ _ 3
2 _ _ _ 7 5 _ _ _
_ 3 _ _ 4 1 _ _ _
_ _ _ 2 8 _ _ _ 4
Answer: 4 7 8 1 5 2 6 3 9
5 9 3 4 6 7 2 8 1
6 1 2 3 9 8 4 5 7
1 2 4 8 3 6 7 9 5
3 5 9 7 1 4 8 2 6
7 8 6 5 2 9 1 4 3
2 4 1 9 7 5 3 6 8
8 3 5 6 4 1 9 7 2
9 6 7 2 8 3 5 1 4
Metadata: {'puzzle': [[4, 0, 0, 0, 5, 2, 0, 3, 0], [0, 0, 3, 4, 6, 0, 0, 0, 0], [6, 1, 2, 0, 0, 8, 4, 0, 0], [1, 0, 0, 0, 0, 0, 7, 9, 5], [3, 0, 0, 7, 1, 0, 0, 2, 6], [7, 0, 0, 5, 0, 0, 0, 0, 3], [2, 0, 0, 0, 7, 5, 0, 0, 0], [0, 3, 0, 0, 4, 1, 0, 0, 0], [0, 0, 0, 2, 8, 0, 0, 0, 4]], 'solution': [[4, 7, 8, 1, 5, 2, 6, 3, 9], [5, 9, 3, 4, 6, 7, 2, 8, 1], [6, 1, 2, 3, 9, 8, 4, 5, 7], [1, 2, 4, 8, 3, 6, 7, 9, 5], [3, 5, 9, 7, 1, 4, 8, 2, 6], [7, 8, 6, 5, 2, 9, 1, 4, 3], [2, 4, 1, 9, 7, 5, 3, 6, 8], [8, 3, 5, 6, 4, 1, 9, 7, 2], [9, 6, 7, 2, 8, 3, 5, 1, 4]], 'num_empty': 48}

Example 2:
Question: Solve this Sudoku puzzle:
_ _ _ 1 3 2 6 4 5
_ 4 _ 7 _ _ _ 9 1
_ _ 1 8 _ 9 _ _ _
_ 8 9 _ _ _ 7 5 4
_ 3 _ 4 _ 1 9 8 _
4 6 _ 5 9 _ 1 2 3
5 _ 4 9 1 7 3 _ _
9 7 6 _ 8 4 5 1 _
8 _ 3 _ _ _ 4 7 _
Answer: 7 9 8 1 3 2 6 4 5
3 4 2 7 5 6 8 9 1
6 5 1 8 4 9 2 3 7
1 8 9 6 2 3 7 5 4
2 3 5 4 7 1 9 8 6
4 6 7 5 9 8 1 2 3
5 2 4 9 1 7 3 6 8
9 7 6 3 8 4 5 1 2
8 1 3 2 6 5 4 7 9
Metadata: {'puzzle': [[0, 0, 0, 1, 3, 2, 6, 4, 5], [0, 4, 0, 7, 0, 0, 0, 9, 1], [0, 0, 1, 8, 0, 9, 0, 0, 0], [0, 8, 9, 0, 0, 0, 7, 5, 4], [0, 3, 0, 4, 0, 1, 9, 8, 0], [4, 6, 0, 5, 9, 0, 1, 2, 3], [5, 0, 4, 9, 1, 7, 3, 0, 0], [9, 7, 6, 0, 8, 4, 5, 1, 0], [8, 0, 3, 0, 0, 0, 4, 7, 0]], 'solution': [[7, 9, 8, 1, 3, 2, 6, 4, 5], [3, 4, 2, 7, 5, 6, 8, 9, 1], [6, 5, 1, 8, 4, 9, 2, 3, 7], [1, 8, 9, 6, 2, 3, 7, 5, 4], [2, 3, 5, 4, 7, 1, 9, 8, 6], [4, 6, 7, 5, 9, 8, 1, 2, 3], [5, 2, 4, 9, 1, 7, 3, 6, 8], [9, 7, 6, 3, 8, 4, 5, 1, 2], [8, 1, 3, 2, 6, 5, 4, 7, 9]], 'num_empty': 34}

Example 3:
Question: Solve this Sudoku puzzle:
_ _ 1 2 3 _ _ _ 9
3 _ _ 1 8 5 6 7 2
_ _ _ 4 9 6 1 _ _
1 _ 5 7 _ _ 9 2 _
_ 4 _ _ 5 9 7 1 6
9 _ 6 _ 1 _ 4 5 3
_ _ 3 9 7 _ 2 8 4
_ _ 2 6 4 _ _ 9 1
_ 1 _ 5 2 8 3 _ _
Answer: 5 6 1 2 3 7 8 4 9
3 9 4 1 8 5 6 7 2
8 2 7 4 9 6 1 3 5
1 3 5 7 6 4 9 2 8
2 4 8 3 5 9 7 1 6
9 7 6 8 1 2 4 5 3
6 5 3 9 7 1 2 8 4
7 8 2 6 4 3 5 9 1
4 1 9 5 2 8 3 6 7
Metadata: {'puzzle': [[0, 0, 1, 2, 3, 0, 0, 0, 9], [3, 0, 0, 1, 8, 5, 6, 7, 2], [0, 0, 0, 4, 9, 6, 1, 0, 0], [1, 0, 5, 7, 0, 0, 9, 2, 0], [0, 4, 0, 0, 5, 9, 7, 1, 6], [9, 0, 6, 0, 1, 0, 4, 5, 3], [0, 0, 3, 9, 7, 0, 2, 8, 4], [0, 0, 2, 6, 4, 0, 0, 9, 1], [0, 1, 0, 5, 2, 8, 3, 0, 0]], 'solution': [[5, 6, 1, 2, 3, 7, 8, 4, 9], [3, 9, 4, 1, 8, 5, 6, 7, 2], [8, 2, 7, 4, 9, 6, 1, 3, 5], [1, 3, 5, 7, 6, 4, 9, 2, 8], [2, 4, 8, 3, 5, 9, 7, 1, 6], [9, 7, 6, 8, 1, 2, 4, 5, 3], [6, 5, 3, 9, 7, 1, 2, 8, 4], [7, 8, 2, 6, 4, 3, 5, 9, 1], [4, 1, 9, 5, 2, 8, 3, 6, 7]], 'num_empty': 33}

syllogism

Generates syllogism reasoning tasks

Default configuration:

allow_all = True
allow_no = True
allow_some = True
allow_some_not = True
invalid_ratio = 0.3
inversion_probability = 0.3
seed = 42
size = 500

Example tasks:

Example 1:
Question: Consider these statements:
1. No students are humans
2. All humans are chefs

Does it logically follow that:
Some chefs are humans?
(Answer Yes or No)
Answer: Yes
Metadata: {'premise1': 'No students are humans', 'premise2': 'All humans are chefs', 'selected_premise': 2, 'conclusion': 'Some chefs are humans', 'is_valid': True, 'type': 'inversion'}

Example 2:
Question: Consider these statements:
1. All children are animals
2. Some animals are not doctors

Does it logically follow that:
Some children are not doctors?
(Answer Yes or No)
Answer: Yes
Metadata: {'premise1': 'All children are animals', 'premise2': 'Some animals are not doctors', 'conclusion': 'Some children are not doctors', 'is_valid': True, 'type': 'syllogism'}

Example 3:
Question: Consider these statements:
1. Some butterflies are not tigers
2. No tigers are whales

Does it logically follow that:
Some butterflies are whales?
(Answer Yes or No)
Answer: No
Metadata: {'premise1': 'Some butterflies are not tigers', 'premise2': 'No tigers are whales', 'conclusion': 'Some butterflies are whales', 'is_valid': False, 'type': 'syllogism'}

time_intervals

Generates time interval calculation tasks with various formats and complexities

Default configuration:

min_time = 00:00:00
max_time = 23:59:59.999999
max_time_difference_seconds = 86400
min_date = 1900-01-01
max_date = 3000-01-01
max_date_difference_days = 100
task_types = ['time', 'time_seconds', 'time_ms', 'date', 'datetime', 'datetime_tz']
seed = 42
size = 500

Example tasks:

Example 1:
Question: A system backup started at 2964-06-17 08:15:14 and completed at 2964-07-04 11:59:09. What was the total backup duration? Answer in D days, HH:MM.
Answer: 17 days, 03:43
Metadata: {'task_type': 'datetime_tz', 'start_time': datetime.datetime(2964, 6, 17, 8, 15, 14), 'end_time': datetime.datetime(2964, 7, 4, 11, 59, 9), 'format': '%Y-%m-%d %H:%M:%S', 'expected_format': 'D days, HH:MM'}

Example 2:
Question: A video call started at 09:44 and ended at 12:22. How long was the call? Answer in HH:MM.
Answer: 02:38
Metadata: {'task_type': 'time', 'start_time': datetime.datetime(2025, 2, 14, 9, 44), 'end_time': datetime.datetime(2025, 2, 14, 12, 22), 'format': '%H:%M', 'expected_format': 'HH:MM'}

Example 3:
Question: Calculate the time difference between Sat Dec 22 2677 and Thu Mar 21 2678. Express the result in D days.
Answer: 89 days
Metadata: {'task_type': 'date', 'start_time': datetime.datetime(2677, 12, 22, 0, 0), 'end_time': datetime.datetime(2678, 3, 21, 0, 0), 'format': '%a %b %d %Y', 'expected_format': 'D days'}

tower_of_hanoi

Generates Tower of Hanoi problems with solutions. Supports variable number of pegs using the optimized Frame-Stewart algorithm with Peg State Tracking.

Default configuration:

min_disks = 3
max_disks = 7
min_pegs = 3
max_pegs = 4
size = 500
seed = 42
visualize = False

Example tasks:

Example 1:
Question: Solve the Tower of Hanoi problem with 3 disks and 3 pegs.
Move all disks from Peg 3 to Peg 2 following the rules:
- Only one disk can be moved at a time.
- A larger disk cannot be placed on top of a smaller disk.
- All disks must be on a peg at all times.
Example:
Move disk 1 from Peg 1 to Peg 3
Move disk 2 from Peg 1 to Peg 2
Move disk 1 from Peg 3 to Peg 2

Provide the sequence of moves.
Answer: ['Move disk 1 from Peg 3 to Peg 2', 'Move disk 2 from Peg 3 to Peg 1', 'Move disk 1 from Peg 2 to Peg 1', 'Move disk 3 from Peg 3 to Peg 2', 'Move disk 1 from Peg 1 to Peg 3', 'Move disk 2 from Peg 1 to Peg 2', 'Move disk 1 from Peg 3 to Peg 2']
Metadata: {'num_disks': 3, 'num_pegs': 3, 'start_peg': 3, 'target_peg': 2, 'auxiliary_pegs': [1], 'solution_length': 7}

Example 2:
Question: Solve the Tower of Hanoi problem with 3 disks and 4 pegs.
Move all disks from Peg 2 to Peg 4 following the rules:
- Only one disk can be moved at a time.
- A larger disk cannot be placed on top of a smaller disk.
- All disks must be on a peg at all times.
Example:
Move disk 1 from Peg 1 to Peg 3
Move disk 2 from Peg 1 to Peg 2
Move disk 1 from Peg 3 to Peg 2

Provide the sequence of moves.
Answer: ['Move disk 1 from Peg 2 to Peg 1', 'Move disk 2 from Peg 2 to Peg 3', 'Move disk 3 from Peg 2 to Peg 4', 'Move disk 2 from Peg 3 to Peg 4', 'Move disk 1 from Peg 1 to Peg 4']
Metadata: {'num_disks': 3, 'num_pegs': 4, 'start_peg': 2, 'target_peg': 4, 'auxiliary_pegs': [1, 3], 'solution_length': 5}

Example 3:
Question: Solve the Tower of Hanoi problem with 6 disks and 3 pegs.
Move all disks from Peg 1 to Peg 2 following the rules:
- Only one disk can be moved at a time.
- A larger disk cannot be placed on top of a smaller disk.
- All disks must be on a peg at all times.
Example:
Move disk 1 from Peg 1 to Peg 3
Move disk 2 from Peg 1 to Peg 2
Move disk 1 from Peg 3 to Peg 2

Provide the sequence of moves.
Answer: ['Move disk 1 from Peg 1 to Peg 3', 'Move disk 2 from Peg 1 to Peg 2', 'Move disk 1 from Peg 3 to Peg 2', 'Move disk 3 from Peg 1 to Peg 3', 'Move disk 1 from Peg 2 to Peg 1', 'Move disk 2 from Peg 2 to Peg 3', 'Move disk 1 from Peg 1 to Peg 3', 'Move disk 4 from Peg 1 to Peg 2', 'Move disk 1 from Peg 3 to Peg 2', 'Move disk 2 from Peg 3 to Peg 1', 'Move disk 1 from Peg 2 to Peg 1', 'Move disk 3 from Peg 3 to Peg 2', 'Move disk 1 from Peg 1 to Peg 3', 'Move disk 2 from Peg 1 to Peg 2', 'Move disk 1 from Peg 3 to Peg 2', 'Move disk 5 from Peg 1 to Peg 3', 'Move disk 1 from Peg 2 to Peg 1', 'Move disk 2 from Peg 2 to Peg 3', 'Move disk 1 from Peg 1 to Peg 3', 'Move disk 3 from Peg 2 to Peg 1', 'Move disk 1 from Peg 3 to Peg 2', 'Move disk 2 from Peg 3 to Peg 1', 'Move disk 1 from Peg 2 to Peg 1', 'Move disk 4 from Peg 2 to Peg 3', 'Move disk 1 from Peg 1 to Peg 3', 'Move disk 2 from Peg 1 to Peg 2', 'Move disk 1 from Peg 3 to Peg 2', 'Move disk 3 from Peg 1 to Peg 3', 'Move disk 1 from Peg 2 to Peg 1', 'Move disk 2 from Peg 2 to Peg 3', 'Move disk 1 from Peg 1 to Peg 3', 'Move disk 6 from Peg 1 to Peg 2', 'Move disk 1 from Peg 3 to Peg 2', 'Move disk 2 from Peg 3 to Peg 1', 'Move disk 1 from Peg 2 to Peg 1', 'Move disk 3 from Peg 3 to Peg 2', 'Move disk 1 from Peg 1 to Peg 3', 'Move disk 2 from Peg 1 to Peg 2', 'Move disk 1 from Peg 3 to Peg 2', 'Move disk 4 from Peg 3 to Peg 1', 'Move disk 1 from Peg 2 to Peg 1', 'Move disk 2 from Peg 2 to Peg 3', 'Move disk 1 from Peg 1 to Peg 3', 'Move disk 3 from Peg 2 to Peg 1', 'Move disk 1 from Peg 3 to Peg 2', 'Move disk 2 from Peg 3 to Peg 1', 'Move disk 1 from Peg 2 to Peg 1', 'Move disk 5 from Peg 3 to Peg 2', 'Move disk 1 from Peg 1 to Peg 3', 'Move disk 2 from Peg 1 to Peg 2', 'Move disk 1 from Peg 3 to Peg 2', 'Move disk 3 from Peg 1 to Peg 3', 'Move disk 1 from Peg 2 to Peg 1', 'Move disk 2 from Peg 2 to Peg 3', 'Move disk 1 from Peg 1 to Peg 3', 'Move disk 4 from Peg 1 to Peg 2', 'Move disk 1 from Peg 3 to Peg 2', 'Move disk 2 from Peg 3 to Peg 1', 'Move disk 1 from Peg 2 to Peg 1', 'Move disk 3 from Peg 3 to Peg 2', 'Move disk 1 from Peg 1 to Peg 3', 'Move disk 2 from Peg 1 to Peg 2', 'Move disk 1 from Peg 3 to Peg 2']
Metadata: {'num_disks': 6, 'num_pegs': 3, 'start_peg': 1, 'target_peg': 2, 'auxiliary_pegs': [3], 'solution_length': 63}

tsumego

Generates Tsumego problems with configurable parameters

Default configuration:

min_board_size = 9
max_board_size = 13
max_stones = 15
size = 500
seed = 42

Example tasks:

Example 1:
Question: I have a Go problem for you. Black moves next - can you capture some of the white stones?

   A B C D E F G H I
 9 X . . . X . . . .
 8 . . . . . . . . .
 7 . O . O . . X . .
 6 . . . X . . . . O
 5 O . X O X . . . .
 4 . X O O . O . . .
 3 . . X O X . . . .
 2 . . . X . . . . .
 1 . O . O . . X . .

X - Black
O - White

Specify your move in coordinates (e.g. 'C4' for column C, row 4)
Answer: E4
Metadata: {'difficulty': {'board_size': 9}, 'board': [['X', '.', '.', '.', 'X', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', 'O', '.', 'O', '.', '.', 'X', '.', '.'], ['.', '.', '.', 'X', '.', '.', '.', '.', 'O'], ['O', '.', 'X', 'O', 'X', '.', '.', '.', '.'], ['.', 'X', 'O', 'O', '.', 'O', '.', '.', '.'], ['.', '.', 'X', 'O', 'X', '.', '.', '.', '.'], ['.', '.', '.', 'X', '.', '.', '.', '.', '.'], ['.', 'O', '.', 'O', '.', '.', 'X', '.', '.']], 'solution': 'E4'}

Example 2:
Question: Here's a Go challenge. Playing as Black, how can you capture as many white stones as possible?

   A B C D E F G H I
 9 . . O . . . . . .
 8 . X O . . . . . .
 7 X . X . . . . . .
 6 O O O X . . . . .
 5 X O O . . . . . .
 4 . X . . . . . . O
 3 . X . . . . X . .
 2 O . O . . . . . .
 1 . . . . O . . . .

X - Black
O - White

Specify your move in coordinates (e.g. 'C4' for column C, row 4)
Answer: B7
Metadata: {'difficulty': {'board_size': 9}, 'board': [['.', '.', 'O', '.', '.', '.', '.', '.', '.'], ['.', 'X', 'O', '.', '.', '.', '.', '.', '.'], ['X', '.', 'X', '.', '.', '.', '.', '.', '.'], ['O', 'O', 'O', 'X', '.', '.', '.', '.', '.'], ['X', 'O', 'O', '.', '.', '.', '.', '.', '.'], ['.', 'X', '.', '.', '.', '.', '.', '.', 'O'], ['.', 'X', '.', '.', '.', '.', 'X', '.', '.'], ['O', '.', 'O', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', 'O', '.', '.', '.', '.']], 'solution': 'B7'}

Example 3:
Question: Tsumego time. Black to play and capture some stones.
Find the key move.

   A B C D E F G H I J K L
12 . . . . . . . . . . . .
11 . . X . . . . . . . . .
10 . . . . . . . . . . . .
 9 . . . . . . . . . . . .
 8 X . . . . X . . . X . .
 7 . X . . . . . . . . . .
 6 . O X X . . . . . . . O
 5 . X O O X . . . . . . .
 4 . O O . . . . . O . . O
 3 X . X . . . . . . . . .
 2 . . . . . . . . . . . .
 1 . . . . . . . . . . X .

X - Black
O - White

Specify your move in coordinates (e.g. 'C4' for column C, row 4)
Answer: D4
Metadata: {'difficulty': {'board_size': 12}, 'board': [['.', '.', '.', '.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', 'X', '.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.', '.', '.', '.'], ['X', '.', '.', '.', '.', 'X', '.', '.', '.', 'X', '.', '.'], ['.', 'X', '.', '.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', 'O', 'X', 'X', '.', '.', '.', '.', '.', '.', '.', 'O'], ['.', 'X', 'O', 'O', 'X', '.', '.', '.', '.', '.', '.', '.'], ['.', 'O', 'O', '.', '.', '.', '.', '.', 'O', '.', '.', 'O'], ['X', '.', 'X', '.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.', '.', 'X', '.']], 'solution': 'D4'}

word_ladder

Generates word ladder transformation tasks

Default configuration:

min_word_length = 4
max_word_length = 4
min_chain_length = -1
max_chain_length = -1
seed = 42
size = 500

Example tasks:

Example 1:
Question: Transform the word ladder 'HAND' to 'GLEE' by changing one letter at a time.
Answer: HAND,HARD,HERD,HEED,FEED,FLED,FLEE,GLEE
Metadata: {'start_word': 'HAND', 'end_word': 'GLEE', 'word_length': 4, 'chain_length': 8}

Example 2:
Question: Transform the word ladder 'JAZZ' to 'DORM' by changing one letter at a time.
Answer: JAZZ,JIZZ,FIZZ,FUZZ,FUZE,FAZE,FARE,FORE,FORM,DORM
Metadata: {'start_word': 'JAZZ', 'end_word': 'DORM', 'word_length': 4, 'chain_length': 10}

Example 3:
Question: Transform the word ladder 'SNOG' to 'SUQS' by changing one letter at a time.
Answer: SNOG,SNOW,SHOW,SHEW,SHES,SUES,SUQS
Metadata: {'start_word': 'SNOG', 'end_word': 'SUQS', 'word_length': 4, 'chain_length': 7}

word_sequence_reversal

Generates word sequence reversal tasks from text spans

Default configuration:

min_words = 3
max_words = 8
seed = 42
size = 500

Example tasks:

Example 1:
Question: Reverse this list of words: bed, if, problem, but, Well, an, transmission, nutritive
Answer: nutritive, transmission, an, Well, but, problem, if, bed
Metadata: {'num_words': 8, 'words': ['bed', 'if', 'problem', 'but', 'Well', 'an', 'transmission', 'nutritive']}

Example 2:
Question: Reverse this list of words: it, pleasure, Gutenberg
Answer: Gutenberg, pleasure, it
Metadata: {'num_words': 3, 'words': ['it', 'pleasure', 'Gutenberg']}

Example 3:
Question: Reverse this list of words: readable, to, he, that, to, possession
Answer: possession, to, that, he, to, readable
Metadata: {'num_words': 6, 'words': ['readable', 'to', 'he', 'that', 'to', 'possession']}

word_sorting

Generates word sorting tasks

Default configuration:

min_words = 3
max_words = 10
min_word_length = 3
max_word_length = 12
transformation = original
seed = 42
size = 500

Example tasks:

Example 1:
Question: Sort these words in ascending order (using ASCII/Unicode ordering) and return them as a comma-separated list:
DIRECT, given, exclaims, dreaming
Answer: DIRECT, dreaming, exclaims, given
Metadata: {'original_words': ['DIRECT', 'given', 'exclaims', 'dreaming'], 'transformed_words': ['DIRECT', 'given', 'exclaims', 'dreaming'], 'direction': 'ascending', 'transformation': <TextTransformation.ORIGINAL: 'original'>, 'sorted_words': ['DIRECT', 'dreaming', 'exclaims', 'given']}

Example 2:
Question: Sort these words in descending order (using ASCII/Unicode ordering) and return them as a comma-separated list:
heat, begun, sometimes
Answer: sometimes, heat, begun
Metadata: {'original_words': ['heat', 'begun', 'sometimes'], 'transformed_words': ['heat', 'begun', 'sometimes'], 'direction': 'descending', 'transformation': <TextTransformation.ORIGINAL: 'original'>, 'sorted_words': ['sometimes', 'heat', 'begun']}

Example 3:
Question: Sort these words in ascending order (using ASCII/Unicode ordering) and return them as a comma-separated list:
violates, yes, already, completing, pages, duty, his, EXPRESS, duly
Answer: EXPRESS, already, completing, duly, duty, his, pages, violates, yes
Metadata: {'original_words': ['violates', 'yes', 'already', 'completing', 'pages', 'duty', 'his', 'EXPRESS', 'duly'], 'transformed_words': ['violates', 'yes', 'already', 'completing', 'pages', 'duty', 'his', 'EXPRESS', 'duly'], 'direction': 'ascending', 'transformation': <TextTransformation.ORIGINAL: 'original'>, 'sorted_words': ['EXPRESS', 'already', 'completing', 'duly', 'duty', 'his', 'pages', 'violates', 'yes']}

zebra_puzzles

Generates Zebra Puzzles with configurable parameters

Default configuration:

num_people = 4
num_characteristics = 4
seed = 42
size = 500

Example tasks:

Example 1:
Question: This is a logic puzzle. There are 4 houses (numbered 1 on the left, 4 on the right), from the perspective of someone standing across the street from them. Each has a different person in them. They have different characteristics:
 - Each person has a unique name: carol, arnold, alice, bob
 - People use different phone models: huawei p50, samsung galaxy s21, oneplus 9, google pixel 6
 - Each person has a favorite drink: milk, boba tea, coffee, water
 - The people keep different animals: bird, cat, fish, dog

1. Alice is the cat lover.
2. The person who likes milk is in the third house.
3. The person who uses a Huawei P50 is Bob.
4. The one who only drinks water is the bird keeper.
5. The cat lover is in the second house.
6. The boba tea drinker is the dog owner.
7. The person who uses a Google Pixel 6 is directly left of Carol.
8. The one who only drinks water is Carol.
9. Carol is the person who uses a OnePlus 9.

What is Name of the person who lives in House 1?
Answer: bob
Metadata: {'num_people': 4, 'num_characteristics': 4}

Example 2:
Question: This is a logic puzzle. There are 4 houses (numbered 1 on the left, 4 on the right), from the perspective of someone standing across the street from them. Each has a different person in them. They have different characteristics:
 - Each person has a unique name: alice, bob, arnold, carol
 - Each mother is accompanied by their child: alice, bella, billy, timothy
 - The people are of nationalities: brit, german, chinese, dane
 - Everyone has something different for lunch: soup, stir fry, grilled cheese, pizza

1. The British person is Arnold.
2. The person's child is named Alice is directly left of the person who loves the soup.
3. The person who loves stir fry is the person's child is named Bella.
4. The Chinese is Carol.
5. The German is the person's child is named Bella.
6. The person's child is named Bella is Bob.
7. The person who loves the soup is in the second house.
8. The person who loves the soup is the British person.
9. The person's child is named Alice is Carol.
10. The British person is directly left of the German.
11. The person who is the mother of Billy is the person who is a pizza lover.

What is Name of the person who lives in House 1?
Answer: carol
Metadata: {'num_people': 4, 'num_characteristics': 4}

Example 3:
Question: This is a logic puzzle. There are 4 houses (numbered 1 on the left, 4 on the right), from the perspective of someone standing across the street from them. Each has a different person in them. They have different characteristics:
 - Each person has a unique name: alice, arnold, bob, carol
 - Everyone has a different favorite cigar: pall mall, dunhill, blue master, prince
 - Everyone has something different for lunch: stir fry, grilled cheese, soup, pizza
 - Each person has a favorite color: blue, purple, brown, white

1. The person who loves white is the person who loves stir fry.
2. The person who loves brown is directly left of the Prince smoker.
3. The person who is a pizza lover and Arnold are next to each other.
4. The person partial to Pall Mall is the person who loves white.
5. Alice is the person who loves the soup.
6. The person partial to Pall Mall is directly left of the person who loves the soup.
7. The person who smokes Blue Master is directly left of the Dunhill smoker.
8. The Dunhill smoker is Bob.
9. The person who loves the soup is the person who loves blue.

What is Name of the person who lives in House 1?
Answer: carol
Metadata: {'num_people': 4, 'num_characteristics': 4}

239 KiB Raw Blame History Unescape Escape

Reasoning Gym Dataset Gallery

Available Datasets

Dataset Examples

ab

advanced_geometry

aiw

arc_1d

arc_agi

base_conversion

basic_arithmetic

bf

binary_matrix

caesar_cipher

calendar_arithmetic

chain_sum

color_cube_rotation

complex_arithmetic

count_bits

count_primes

countdown

course_schedule

dice

family_relationships

figlet_font

fraction_simplification

game_of_life

gcd

graph_color

group_anagrams

gsm_symbolic

intermediate_integration

isomorphic_strings

knight_swap

largest_island

lcm

leg_counting

letter_counting

letter_jumble

manipulate_matrix

maze

mini_sudoku

n_queens

number_filtering

number_sequence

number_sorting

palindrome

polynomial_equations

polynomial_multiplication

pool_matrix

power_function

prime_factorization

products

propositional_logic

quantum_lock

ransom_note

rearc

rectangle_count

rotate_matrix

rubiks_cube

self_reference

sentence_reordering

simple_equations

simple_geometry

simple_integration

sokoban

spell_backward

spiral_matrix

string_insertion

string_manipulation

string_synthesis

sudoku

syllogism

time_intervals

tower_of_hanoi

tsumego

word_ladder

word_sequence_reversal

word_sorting

zebra_puzzles

239 KiB

Raw Blame History