Draft:Bpow45

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?

Problem by Alberto L Delgado, from the now extinct Bradley Problem of the Week.