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# Reasoning Gym Dataset Gallery
This gallery shows examples from all available datasets using their default configurations.
## Available Datasets
- [base_conversion](#base_conversion)
- [basic_arithmetic](#basic_arithmetic)
- [bf](#bf)
- [caesar_cipher](#caesar_cipher)
- [chain_sum](#chain_sum)
- [color_cube_rotation](#color_cube_rotation)
- [countdown](#countdown)
- [family_relationships](#family_relationships)
- [figlet_font](#figlet_font)
- [fraction_simplification](#fraction_simplification)
- [game_of_life](#game_of_life)
- [gcd](#gcd)
- [lcm](#lcm)
- [leg_counting](#leg_counting)
- [letter_counting](#letter_counting)
- [letter_jumble](#letter_jumble)
- [maze](#maze)
- [mini_sudoku](#mini_sudoku)
- [number_filtering](#number_filtering)
- [number_sequence](#number_sequence)
- [number_sorting](#number_sorting)
- [polynomial_equations](#polynomial_equations)
- [prime_factorization](#prime_factorization)
- [propositional_logic](#propositional_logic)
- [quantum_lock](#quantum_lock)
- [rubiks_cube](#rubiks_cube)
- [sentence_reordering](#sentence_reordering)
- [simple_equations](#simple_equations)
- [spell_backward](#spell_backward)
- [sudoku](#sudoku)
- [syllogism](#syllogism)
- [word_sequence_reversal](#word_sequence_reversal)
- [word_sorting](#word_sorting)
## Dataset Examples
### base_conversion
Generates base conversion tasks
Default configuration:
```python
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 28e to binary
Answer: 1010001110
Metadata: {'decimal_value': 654, 'source_base': 3, 'target_base': 2, 'source_repr': '28e', 'target_repr': '1010001110'}
Example 2:
Question: Convert the base-6 number 27 to base-13 (use lowercase letters a-z for digits above 9)
Answer: 27
Metadata: {'decimal_value': 39, 'source_base': 6, 'target_base': 13, 'source_repr': '27', 'target_repr': '27'}
Example 3:
Question: Convert the base-10 number 1a2 to base-13 (use lowercase letters a-z for digits above 9)
Answer: 1a2
Metadata: {'decimal_value': 418, 'source_base': 10, 'target_base': 13, 'source_repr': '1a2', 'target_repr': '1a2'}
```
### basic_arithmetic
Dataset that generates basic arithmetic tasks with configurable complexity
Default configuration:
```python
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:
```python
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': '>[-]>[-]<>+++++++++[<+++++++++++++>-]<.-------.----------.+.+++++++++++++.<'}
```
### caesar_cipher
Generates Caesar cipher encryption/decryption tasks
Default configuration:
```python
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'}
```
### chain_sum
Generates simple arithmetic tasks using only + and - operators
Default configuration:
```python
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: {'num_terms': 2, 'num_digits': 1, 'expression': '4 + 3'}
Example 2:
Question: 812 + 880 =
Answer: 1692
Metadata: {'num_terms': 2, 'num_digits': 3, 'expression': '812 + 880'}
Example 3:
Question: 2 + 6 + 3 + 4 + 0 =
Answer: 15
Metadata: {'num_terms': 5, 'num_digits': 1, 'expression': '2 + 6 + 3 + 4 + 0'}
```
### color_cube_rotation
Generates color cube rotation reasoning tasks
Default configuration:
```python
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}
```
### countdown
Generates Countdown Number Game tasks
Default configuration:
```python
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'}
```
### family_relationships
Generates family relationship reasoning tasks
Default configuration:
```python
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:
```python
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:
```python
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:
```python
grid_size_x = 20
grid_size_y = 20
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?
[[0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 1 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 1 0 0 1 0 1 1 0]
[1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0]
[0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0]
[0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0]
[1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0]
[1 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1]
[1 1 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1]
[0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0]
[1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0]
[1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1]
[0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0]
[0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0]]
Answer: [[0 0 1 1 1 0 1 1 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 0 0 0 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0]
[0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0]
[0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0]
[0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 1 1 1 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1]
[1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1]
[1 1 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0]
[0 0 0 0 0 0 1 0 1 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 1]
[1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1]
[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1]
[1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 1 1 0 0 0 0 0 1 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 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]]
Metadata: {'grid_size_x': 20, 'grid_size_y': 20, 'filled_cells': 100, 'simulation_steps': 1}
Example 2:
Question: What will this Game of Life board look like after 1 steps of simulation?
[[1 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0]
[0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0]
[0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0]
[0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1]
[0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0]
[1 1 0 0 0 0 1 0 0 1 0 1 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 0]
[0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0]
[0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1]
[0 0 1 1 1 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1]
[0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1]
[0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1]
[0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1]
[0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1]
[0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0]
[0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0]]
Answer: [[0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1]
[0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 1]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[1 1 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 1 1 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 1 0 0 0]
[0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0]
[1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1]
[1 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0]
[1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]]
Metadata: {'grid_size_x': 20, 'grid_size_y': 20, 'filled_cells': 100, 'simulation_steps': 1}
Example 3:
Question: What will this Game of Life board look like after 1 steps of simulation?
[[0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1]
[0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 1]
[0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0]
[0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 1]
[0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0]
[1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1]
[0 0 0 1 0 0 0 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 1 1 0 0 1 0]
[0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0]
[0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0]
[0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0]
[1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0]]
Answer: [[1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1]
[0 0 1 1 0 0 0 1 0 0 0 1 1 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 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 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 1 1 1 0 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 0 1 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1]
[0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1]
[0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0]
[0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0]
[0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0]]
Metadata: {'grid_size_x': 20, 'grid_size_y': 20, 'filled_cells': 100, 'simulation_steps': 1}
```
### gcd
Generates Greatest Common Divisor (GCD) tasks
Default configuration:
```python
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}
```
### lcm
Generates Least Common Multiple (LCM) tasks
Default configuration:
```python
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:
```python
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: {'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: {'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: {'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:
```python
min_words = 5
max_words = 15
seed = 42
size = 500
```
Example tasks:
```
Example 1:
Question: How many times does the letter "w" appear in the text: "bed and enters his mechanical dresser Two minutes later the machine deposited him all dressed"?
Answer: 1
Metadata: {'span_length': 15, 'target_letter': 'w', '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 "p" appear in the text: "it into a watering place"?
Answer: 1
Metadata: {'span_length': 5, 'target_letter': 'p', '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:
```python
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']}
```
### maze
Generates mazes with guaranteed shortest path distance from start to goal
within [min_dist, max_dist].
Default configuration:
```python
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:
```python
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}
```
### number_filtering
Generates number filtering tasks
Default configuration:
```python
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']
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']
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']
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:
```python
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:
```python
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
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
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
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']}
```
### 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:
```python
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 u in the equation: -127*u = 0
Answer: [0.0]
Metadata: {'polynomial_expr': '-127*u', 'variable': 'u', 'degree': 1, 'real_solutions': [0.0]}
Example 2:
Question: Determine the real value(s) of b tha satisfies: 86*b**2 - 2*b - 13 = 0
Answer: [-0.3773425275273891, 0.4005983414808775]
Metadata: {'polynomial_expr': '86*b**2 - 2*b - 13', 'variable': 'b', 'degree': 2, 'real_solutions': [-0.3773425275273891, 0.4005983414808775]}
Example 3:
Question: Determine the real value(s) of n tha satisfies: 71*n**3 - 2*n - 29 = 0
Answer: [0.7546129960163634]
Metadata: {'polynomial_expr': '71*n**3 - 2*n - 29', 'variable': 'n', 'degree': 3, 'real_solutions': [0.7546129960163634]}
```
### prime_factorization
Generates prime factorization tasks
Default configuration:
```python
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]}
```
### propositional_logic
Generates propositional logic reasoning tasks
Default configuration:
```python
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:
```python
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.
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.
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.
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}
```
### rubiks_cube
Generates RubiksCube tasks
Default configuration:
```python
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'"}
```
### sentence_reordering
Generates sentence reordering tasks from text spans
Default configuration:
```python
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:
```python
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'}
```
### spell_backward
Generates tasks to spell words backward
Default configuration:
```python
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}
```
### sudoku
Generates sudoku puzzles with configurable difficulty
Default configuration:
```python
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:
```python
terms = None
allow_all = True
allow_no = True
allow_some = True
allow_some_not = True
include_invalid = True
invalid_ratio = 0.3
seed = 42
size = 500
```
Example tasks:
```
Example 1:
Question: Consider these statements:
1. No students are humans
2. No humans are chefs
Does it logically follow that:
No students are chefs?
(Answer Yes or No)
Answer: Yes
Metadata: {'premise1': 'No students are humans', 'premise2': 'No humans are chefs', 'conclusion': 'No students are chefs', 'is_valid': True}
Example 2:
Question: Consider these statements:
1. Some ... are not children are animals
2. Some animals are doctors
Does it logically follow that:
All children are doctors?
(Answer Yes or No)
Answer: Yes
Metadata: {'premise1': 'Some ... are not children are animals', 'premise2': 'Some animals are doctors', 'conclusion': 'All children are doctors', 'is_valid': True}
Example 3:
Question: Consider these statements:
1. All butterflies are tigers
2. No tigers are whales
Does it logically follow that:
Some ... are not butterflies are whales?
(Answer Yes or No)
Answer: No
Metadata: {'premise1': 'All butterflies are tigers', 'premise2': 'No tigers are whales', 'conclusion': 'Some ... are not butterflies are whales', 'is_valid': False}
```
### word_sequence_reversal
Generates word sequence reversal tasks from text spans
Default configuration:
```python
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:
```python
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:
due, ever, many, generations
Answer: due, ever, generations, many
Metadata: {'original_words': ['due', 'ever', 'many', 'generations'], 'transformed_words': ['due', 'ever', 'many', 'generations'], 'direction': 'ascending', 'transformation': <TextTransformation.ORIGINAL: 'original'>, 'sorted_words': ['due', 'ever', 'generations', 'many']}
Example 2:
Question: Sort these words in descending order (using ASCII/Unicode ordering) and return them as a comma-separated list:
change, 250, young
Answer: young, change, 250
Metadata: {'original_words': ['change', '250', 'young'], 'transformed_words': ['change', '250', 'young'], 'direction': 'descending', 'transformation': <TextTransformation.ORIGINAL: 'original'>, 'sorted_words': ['young', 'change', '250']}
Example 3:
Question: Sort these words in ascending order (using ASCII/Unicode ordering) and return them as a comma-separated list:
industry, elementary, traverse, stepped, meals, rub, resultant, etheric, irritation
Answer: elementary, etheric, industry, irritation, meals, resultant, rub, stepped, traverse
Metadata: {'original_words': ['industry', 'elementary', 'traverse', 'stepped', 'meals', 'rub', 'resultant', 'etheric', 'irritation'], 'transformed_words': ['industry', 'elementary', 'traverse', 'stepped', 'meals', 'rub', 'resultant', 'etheric', 'irritation'], 'direction': 'ascending', 'transformation': <TextTransformation.ORIGINAL: 'original'>, 'sorted_words': ['elementary', 'etheric', 'industry', 'irritation', 'meals', 'resultant', 'rub', 'stepped', 'traverse']}
```
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