Python script to solve a math puzzle related to 69

square_and_cube_have_all_digits.py

"""
The number 69 has a remarkable property: it is the only number whose square and cube together
contain every digit exactly once.

Is an AI agent able to write a program to solve this problem? I gave the following prompt to ChatGPT:
"Write a Python script to find a two-digit number whose square and cube together contain all 10 digits."

Here is the code that it produced. The code is well-written, and it actually works!
"""

# This function takes a number and returns its square and cube as strings
def square_and_cube(n):
    square = str(n * n)
    cube = str(n * n * n)
    return square, cube

# This function checks if a square and cube together contain all 10 digits
def check_square_and_cube(square, cube):
    digits = "0123456789"
    all_digits_present = True
    for digit in digits:
        if digit not in square and digit not in cube:
            all_digits_present = False
            break
    return all_digits_present

# This is the main function that finds a two-digit number
# whose square and cube together contain all 10 digits
def find_number():
    # Loop through all two-digit numbers
    for i in range(10, 100):
        square, cube = square_and_cube(i)
        if check_square_and_cube(square, cube):
            return i

# Find the number and print it
number = find_number()
print(number)