## Using up to one million tiles how many different "hollow" square laminae can be formed?

### Problem 173

Published on Saturday, 22nd December 2007, 01:00 pm; Solved by 5827; Difficulty rating: 30%We shall define a square lamina to be a square outline with a square "hole" so that the shape possesses vertical and horizontal symmetry. For example, using exactly thirty-two square tiles we can form two different square laminae:

With one-hundred tiles, and not necessarily using all of the tiles at one time, it is possible to form forty-one different square laminae.

Using up to one million tiles how many different square laminae can be formed?