# Palindromic Number Question

1. Mar 31, 2008

### rwinston

Hi all

I was looking q # 4 on ProjectEuler.net, and it is a problem to find the largest palindrome constructed from the product of two three-digit integers.

Now, the answer (spoilers, if you dont want to know ) is 906609. However, I got a different answer, but possibly my logic is incorrect. Can anyone spot a flaw in the following reasoning:

As the upper bound of 2 3-digit numbers, I chose 999^2 = 998001. Hence, by counting down from this to a lower limit (say 100) I should have all of the 3-digit integer products in this range? Thus, by starting at the upper limit and counting down, and then testing each integer at every step for the palindrome property, I should find the largest.

I found a palindrome, 997799 which is > the given answer and < 999^2. However, I cant see the flaw in my logic which would imply that this is incorrect and the given answer is correct. Can anyone point me in the right direction? Thanks!

Last edited: Mar 31, 2008
2. Mar 31, 2008

### CRGreathouse

You found it. 997799 = 11 x 90709 is not the product of two three-digit integers.