In Class Activity
MAT 300, Spring 2004
March 23, 2004
Tiling a Checkerboard
1. Consider a standard checker board (red and black alternating squares, 8 x 8). Can
you cover the entire board with dominos, without any domino overlapping?
2. What if one black square and one red square were removed from the corners of the
board? Can you cover the entire board with non-overlapping dominos?
3. Now cover any one red square and any one black square with a single square tile on
each. Is it possible to cover the remaining portion of the board with dominos? Justify
your answer.
4. Can you prove this is the case for the remainder of any checker board (alternating red
and black squares) of dimension 2n x 2n after one black and one red square have been
covered? Justify your answer.
