
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:
To define successor states, we'll consider all possible operations (+, -, x, /) between each pair of numbers in the input state. Here's the step-by-step process:
Choose two numbers from the input state.
Apply each of the four operations to the chosen numbers.
Replace the chosen numbers in the input state with the result of the operation.
Repeat steps 1-3 for all possible pairs of numbers in the input state.
Here's the Python function to generate successor states:
Python
```
def get_successor_states(state):
    successor_states = []
    for i in range(len(state)):
        for j in range(i+1, len(state)):
            a, b = state[i], state[j]
            new_state = state[:i] + state[i+1:j] + state[j+1:]
            successor_states.append(new_state + [a + b])
            successor_states.append(new_state + [a - b])
            successor_states.append(new_state + [b - a])
            successor_states.append(new_state + [a * b])
            if b != 0:
                successor_states.append(new_state + [a / b])
            if a != 0:
                successor_states.append(new_state + [b / a])
    return successor_states
```
This function generates all possible successor states by applying the four operations to each pair of numbers in the input state. Note that division by zero is avoided by checking if the divisor is non-zero

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:
Here's the Python function to test whether a state is a goal state:
Python
```
def is_goal_state(state):
    return len(state) == 1 and state[0] == 24
``

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 627424, total generated 2706100
