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 × 99. Find the largest palindrome made from the product of two 3-digit numbers.

The Idea

Since there are only 900 3-digit numbers, checking all possibilities of products of 3 digit numbers gives $900^2 = 810,000$ possibilities. To eliminate redundancies, we can check only half (for example $100 \cdot 200 = 200 \cdot 100$). This leaves 40,500 combinations to be checked. After multiplying each pair, we check to see if it is a palindrome and if the number is greater than the current max palindrome.