## Hidden Palindrome

#### Problem

A palindrome is a number which reads the same forwards and backwards. For example, the number 232 is a 3-digit palindrome.

Can you find a square 3-digit palindrome, which is also palindromic when divided by 2?

#### Solution

If it is palindromic when divided by 2, it must be even. For a square number, `n`^{2}, to be even, `n` must be even.

Listing even 3-digit squares:

10^{2} = 100, 12^{2} = 144, 14^{2} = 196, 16^{2} = 256,

18^{2} = 324, 20^{2} = 400, 22^{2} = 484, 24^{2} = 576,

26^{2} = 676, 28^{2} = 784, 30^{2} = 900.

The two candidates are 484 and 676, but as 484/2=242 and 676/2=338, the palindrome we seek is 484.

Problem ID: 163 (Apr 2004) Difficulty: 1 Star