Problem 4

from itertools import product
from typing import Tuple

from project_euler import get_problem_description

get_problem_description(4)

A palindromic number reads the same both ways. The largest palindrome made from the product of two $2$-digit numbers is $9009 = 91 \times 99$.

Find the largest palindrome made from the product of two $3$-digit numbers.

Okay, first let’s create a function for checking if a number is a palindrome.

def is_palindrome(number: int) -> bool:
    num_as_string = str(number)
    return num_as_string == num_as_string[::-1]


assert is_palindrome(101)
assert is_palindrome(9009)
assert not is_palindrome(123)

Okay, so good so far.

Now let’s try and solve the problem.

def product_if_palindrome(numbers: Tuple[int, int]) -> int:
    prod = numbers[0] * numbers[1]
    if is_palindrome(prod):
        return prod
    else:
        return 0


three_digit_numbers = range(100, 1000)
max(
    product_if_palindrome(prod)
    for prod in product(three_digit_numbers, three_digit_numbers)
)

906609

And the answer is correct!