Problem 4: Largest Palindrome Product

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

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

Solution Approach

The solution to this problem can quickly be found through the use of the itertools library in python

import itertools

numbers = range(100, 1000)  # 3-digit numbers
pairs = list(itertools.combinations(numbers, 2))

def is_palindrome(n: int) -> bool:
    s = str(n)
    return s == s[::-1]
  
palindromic_products = [x * y for x, y in pairs if is_palindrome(x * y)]
answer = max(palindromic_products)
print(answer)

Explained line by line:

We start by importing the itertools library, which provides functions that create iterators for efficient looping.
We then create a range of numbers from $100$ to $999$ (inclusive) to represent all $3$-digit numbers.
Using the itertools.combinations function, we generate all possible unique pairs of these $3$-digit numbers. Each pair will be used to calculate their product.
Next, we define a helper function called is_palindrome that takes an integer n as input and returns a boolean indicating whether n is a palindrome. This is done by converting the number to a string and checking if it reads the same forwards and backwards.
We then use a list comprehension to iterate through all the pairs of $3$-digit numbers, calculating their products and filtering out only those products that are palindromic using the is_palindrome function.
Finally, we find the maximum value among the palindromic products using the max function and print the result, which is the largest palindrome made from the product of two $3$-digit numbers.

Running the above code leads to an answer of $906609$