##### 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.