An L-tromino is a figure in the plane made of three equal-sized squares connected in an L-shape:
Consider now the following question: Given a square grid () with exactly one cell occupied, is it possible to tile the remaining area using L-trominos?
The answer is yes and it is quite easy to see why. First, if it is a grid () with one cell occupied then there is nothing to tile and we are done.
For we can divide the square into four sub-squares each of size . The occupied cell must appear in exactly one of these sub-squares and we now place an L-tromino appropriately at the center such that one cell gets occupied in each of the other three sub-squares:
Now each of the sub-squares have exactly one cell occupied and the theorem follows by induction.
As an example, here is a complete tiling for a grid: