mathschallenge.net

Problem

A square lamina can be made from 1, 4, 9, 16, 25, ... unit square tiles. But by placing a square hole in the centre of the lamina it is possible to make a "hollow" square lamina from a non-square number such as 32,

   6² 2² = 36 4 = 32

How many different square laminas can be made from 240 unit square tiles?