Friday, April 18, 2008

Tiling chessboard by L-shaped trominoes

Can you cover all but one square of an n x n chessboard by L-shaped trominoes?

Claim : If n is a power of 2, you can always do it !!

Have fun proving this !!

1 comment:

Pavel said...

L as in:
X
XX

or as in:
X
X
XX
?

I assume the first, since there is no way to cover a 2x2 board with the second + 1. If so, I know an inductive solution. The question is:
Can you fill all but one cube of a (2^n)^3 cube grid with 7/8 cubes filled 2x2x2 pieces? (i. e. remove a single cube from a 2x2x2 cube piece to make a 7/8) Can you place the missing cube anywhere you want in the cube grid?

I'm sure if you can do the 2d solution you can do the 3d, but it's another way to think of it, at least.