The 8x8 Tiled Floor


A bathroom floor comprises 8 rows and 8 columns of squares. The square in the lower right corner has been covered by a black tile. Can the tiling of the rest of the floor be completed, using only white L-shaped tiles that each cover three squares?

Here is one of the white tiles:

        +---+---+
        |       |
        +   +---+
        |   |
        +---+
      

And here is the floor to be covered:

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

I give up, show me the solution.


Last revised on 24 September 2000.