The applet below illustrates a proof of S. Golomb's theorem based on the fact that the L-shaped (or right tromino) is a rep-4 tile. (The term rep-tile has also been introduced by Golomb to describe a shape that is tiled by smaller copies of itself.)
Theorem
A unit square has been removed from a 2n×2n board. The rest of the board can be tiled with L-shaped trominos.
By clicking anywhere in the applet you can define (and redefine) the missing square. The "exponent" parameter defines n, for a 2n×2n board. The number can be changed by clicking a little off it central line.