The 8 by 8 Tiled Floor
Solution

There are many solutions. Here is one tiling: 

        +---+---+---+---+---+---+---+---+
        |       |       |       |       |
        +   +---+   +---+   +---+   +---+
        |   |   |   |   |   |   |   |   |
        +---+   +---+   +---+   +---+   +
        |       |       |       |       |
        +---+---+---+---+---+---+---+---+
        |       |       |       |       |
        +   +---+   +---+   +---+   +---+
        |   |   |   |   |   |   |   |   |
        +---+   +---+   +---+   +---+   +
        |       |       |       |       |
        +---+---+---+---+---+---+---+---+
        |       |   |       |   |       |
        +   +---+   +   +---+   +   +---+
        |   |       |   |       |   | X |
        +---+---+---+---+---+---+---+---+

Now suppose that the bathroom floor comprises 2N rows and 2N columns of squares, and that a single square has been covered by a black tile. Prove that, no matter what positive integer N is, and no matter where the black tile was placed, the tiling of the floor can be completed using white L-shaped tiles.

I give up, show me the solution.

Back to The 8 by 8 Tiled Floor Puzzle.

Last revised on 24 September 2000.