Euler 4

So the other night I was a bit bored and decided to do something to pass the time. I first came across Project Euler a while ago, but had never gone further than problem #1. Boredom is a great motivator and I went through problems #2 thru #9 last night and I decided to post my solutions in search of better ones. Feel free to comment with your suggestions.

Project Euler’s Problem #4 statement is —

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.

Searching downward lets us stop as soon as the remaining products cannot beat the best palindrome already found. Starting the inner loop at a also avoids checking both a * b and b * a.

largest = 0

for a in range(999, 99, -1):
    if a * a <= largest:
        break

    for b in range(a, 99, -1):
        product = a * b
        if product <= largest:
            break
        if str(product) == str(product)[::-1]:
            largest = product

print(largest)

This prints 906609 ($993 \times 913 = 906\,609$).