This is a triomino piece:
(A 2 x 2 cell square with one of the corner cells removed)

Prove that a square, 2^n cells to the side, with one square cell removed from the corner can be covered with triomino pieces without any overlapping or going over the border for any natural value of n. The triominos can be rotated.

(For example if n = 1, the result is a triomino shape to begin with - a 2 x 2 square with one cell removed.)

actually this is a well known problem in combinatorics and the result holds whenever one square are absent, not necessarily the corner one. the key is the partition:
11
13
2334
2244
which is the inductive step.

Posted by theBal on 2002-05-24 12:07:49