Problem of the Week

Cover the squares of a 6 x 6 checkerboard with dominoes.  Notice that in the example on the right, there is a way for you to cut the board and avoid cutting a domino, in fact, there are two ways -- once vertically and once horizontally.  Will that always be the case?  More precisely:
(a)  If you cover a 6 x 6 checkerboard with dominoes will you always be able to cut the board and avoid touching the dominoes?
(b) Can you always do it twice -- once vertically and once horizontally?
(c)  Is this always possible for a square checkerboard of any size?

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