
AutoToS prompt:

The 24 Game is a mathematical card game in which the objective is to find a way to manipulate four integers so that the end result is 24. The game is played with a list of four numbers, and the player must use all four numbers exactly once, using any combination of addition, subtraction, multiplication, or division, to arrive at the number 24. If a state is defined by a list of numbers (4 or less), how are successor states defined? Please think step by step. Then, provide only the Python function that returns a list of successor states for an input state.

Here is an example of an initial state:
[6, 6, 2, 1]

Model response:
Successor States Definition
Given a state with 4 or less numbers, successor states are defined as the states that can be reached by applying a mathematical operation (+, -, *, /) to two numbers in the current state. The two numbers are then replaced by the result of the operation.
Here are the steps to generate successor states:
Choose two numbers from the current state.
Apply each of the four mathematical operations (+, -, *, /) to the two numbers.
For each operation, create a new state by replacing the two numbers with the result of the operation.
Add the new states to the list of successor states.
Python Function: Successor States
Python
```
import itertools
import operator

def get_successor_states(state):
    """
    Returns a list of successor states for the given state.
    
    Args:
        state (list): A list of numbers representing the current state.
    
    Returns:
        list: A list of lists, where each sublist is a successor state.
    """
    successor_states = []
    ops = {
        '+': operator.add,
        '-': operator.sub,
        '*': operator.mul,
        '/': operator.truediv
    }
    
    # Choose two numbers from the current state
    for i, j in itertools.combinations(range(len(state)), 2):
        num1, num2 = state[i], state[j]
        
        # Apply each mathematical operation to the two numbers
        for op, func in ops.items():
            try:
                result = func(num1, num2)
                # Create a new state by replacing the two numbers with the result
                new_state = state[:i] + [result] + state[i+1:j] + state[j+1:]
                successor_states.append(new_state)
                # Also try the operation with num2 as the first operand
                result = func(num2, num1)
                new_state = state[:i] + [result] + state[i+1:j] + state[j+1:]
                successor_states.append(new_state)
            except ZeroDivisionError:
                # Skip division by zero
                continue
    
    return successor_states
```
Example usage:
Python
initial_state = [6, 6, 2, 1]
successor_states = get_successor_states(initial_state)
print(successor_states)
Generated by Meta Llama 3.1-405

AutoToS prompt:

Provide only the python code that tests whether a state is a goal state. 
Example goal state: [24]
Example non-goal state: [24,1]

Model response:
Python
```
def is_goal_state(state):
    """
    Returns True if the state is a goal state, False otherwise.
    
    A goal state is a state with a single number, which is 24.
    
    Args:
        state (list): A list of numbers representing the state.
    
    Returns:
        bool: Whether the state is a goal state.
    """
    return len(state) == 1 and state[0] == 24
```
Generated by Meta Llama 3.1-405

System message:
Goal Soundness Test Passed
Soundness test

System message:
Successor States Soundness Test Passed
Completeness test
Successor Completeness Test Passed
Success: 1352, failure: 0, total expansions 628046, total generated 3603139
