## Square Laminas

#### 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,

6

^{2}2^{2}= 36 4 = 32How many different square laminas can be made from 240 unit square tiles?

Problem ID: 56 (Nov 2001) Difficulty: 2 Star