Create python generator files for gsm symbolic templates

reasoning_gym/arithmetic/gsm_symbolic/generator_19.py

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+from random import Random
+from typing import Dict, Any
+
+def generate_from_variables(name: str, pan: str, initial_kernels: int, time_interval: int,
+                          multiplier_2: int, multiplier_3: int) -> Dict[str, Any]:
+    second_interval = multiplier_2 * initial_kernels
+    third_interval = multiplier_3 * initial_kernels  
+    fourth_interval = third_interval // 2
+    residual = fourth_interval // 4
+    total = initial_kernels + second_interval + third_interval + fourth_interval + residual
+
+    question = f"{name} is popping popcorn for a snack. As the {pan} of kernels heats up, the kernels start popping faster. {initial_kernels} pop in the first {time_interval} seconds of cooking, then {multiplier_2} times that amount in the next {time_interval} seconds. The kernels increase to {multiplier_3} times the initial popping rate in the next {time_interval} seconds, but in the final {time_interval} seconds, the popping slows down to half the rate as the past {time_interval} seconds. After {name} takes the {pan} off the heat, a quarter of the number of kernels that popped in the final {time_interval} seconds of cooking also pop from the residual heat. How many pieces of popcorn does {name} have to eat?"
+
+    answer_cot = f"In the second {time_interval} seconds of cooking, {multiplier_2} * {initial_kernels} = {second_interval} kernels pop.\nIn the third {time_interval} seconds, {multiplier_3} * {initial_kernels} = {third_interval} kernels pop.\nIn the final {time_interval} seconds, {third_interval} / 2 = {fourth_interval} kernels pop.\nAfter cooking, the residual heat makes {fourth_interval} / 4 = {residual} kernels pop.\nThus, {name} has {initial_kernels} + {second_interval} + {third_interval} + {fourth_interval} + {residual} = {total} pieces of popcorn to eat.\n#### {total}"
+
+    return {
+        'question': question,
+        'answer': str(total),
+        'answer_cot': answer_cot,
+        'answer_value': total,
+        'variables': {
+            'name': name,
+            'pan': pan,
+            'initial_kernels': initial_kernels,
+            'time_interval': time_interval,
+            'multiplier_2': multiplier_2,
+            'multiplier_3': multiplier_3,
+            'second_interval': second_interval,
+            'third_interval': third_interval,
+            'fourth_interval': fourth_interval,
+            'residual': residual,
+            'total': total
+        }
+    }
+
+def generate_example(rng: Random, difficulty: float = 1.0) -> Dict[str, Any]:
+    names = ["Garrett", "James", "Michael", "David", "John", "Robert", "William"]
+    pans = ["pan", "pot", "skillet"]
+    
+    name = rng.choice(names)
+    pan = rng.choice(pans)
+    
+    # Generate numbers ensuring divisibility conditions are met
+    initial_kernels = int(rng.randint(10, int(101 * difficulty)) // 10 * 10)
+    time_interval = int(rng.randint(10, int(31 * difficulty)) // 2 * 2)
+    multiplier_2 = rng.randint(2, int(5 * difficulty))
+    
+    # Ensure multiplier_3 > multiplier_2 and results in clean division by 8
+    while True:
+        multiplier_3 = rng.randint(multiplier_2 + 1, int(8 * difficulty))
+        if (multiplier_3 * initial_kernels) % 8 == 0:
+            break
+            
+    result = generate_from_variables(name, pan, initial_kernels, time_interval,
+                                   multiplier_2, multiplier_3)
+    
+    return {
+        'question': result['question'],
+        'answer': result['answer'],
+        'metadata': {
+            'difficulty': difficulty,
+            'answer_value': result['answer_value'], 
+            'answer_cot': result['answer_cot'],
+            'variables': result['variables']
+        }
+    }
+
+def original_example() -> Dict[str, Any]:
+    return generate_from_variables("Garrett", "pan", 20, 30, 3, 4)