mathschallenge.net

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, n², to be even, n must be even.

Listing even 3-digit squares:
10² = 100, 12² = 144, 14² = 196, 16² = 256,
18² = 324, 20² = 400, 22² = 484, 24² = 576,
26² = 676, 28² = 784, 30² = 900.

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