Problem:
Two of the squares of a checkerboard are painted yellow, and the rest are painted green. Two color schemes are equivalent if one can be obtained from the other by applying a rotation in the plane of the board. How many inequivalent color schemes are possible?
Solution:
There are ways to select the positions of the yellow squares. Because quarter-turns can be applied to the board, however, there are fewer than inequivalent color schemes. Color schemes in which the two yellow squares are not diametrically opposed appear in four equivalent forms. Color schemes in which the two yellow squares are diametrically opposed appear in two equivalent forms, and there are such pairs of yellow squares. Thus the number of inequivalent color schemes is
The problems on this page are the property of the MAA's American Mathematics Competitions