I hope somebody can help me with this question. I'm kind of stuck ...
The qn is:
Suppose you are given a "chess-board" that has 2^n rows and 2^n columns. You are given an endless supply of L-shaped tiles - each one is a 2x2 chess-board with the upper right square removed. Now, suppose somebody removes a single, random square from your original chess-board. Show that you can completely cover the remaining squares with your L-shaped pieces, without overlapping any of them.
HINT: If you divide your chess-board in half, vertically and horizontally, you get four smaller versions of the same problem. Can three of these sub-problems combine to leave a handy L-shaped hole?
I started by drawing out the first few defective chess-boards and found that for a 2x2 board you had 1 L shaped piece (triomino) 4x4 --> 5 triominos 8x8 --> 21 "
that pattern seems to suggest that each board will have 4 times the number of triominos the previous board has plus 1. Then I thought this doesn't help me any with this qn....
Maybe some sort of constructive proof would be the way to go? I don't know & I'm not sure how to get started. Could anyone help please?