You have 15 3 × 1 rectangular tiles, plus one “L” shaped tile (made up of three 1 × 1 squares). You would like to use these tiles to cover the floor of your 7 × 7 dorm room. Of course, doing so will leave a 1×1 square missing, but you figure you will put a plant there to cover up the hole.

Prove that such a tiling is possible, but the missing square cannot be adjacent to the wall (i.e., on any side of the square).