by Bill Graham

The members of the local gourmet club would like to have new placemats for their next meeting. On hand, they have lots of equal-sized black and white circular disks that could make nice placemats and have the same number of each color. They decide to join disks together in a rectangular array to make the place mats. The white disks will be used for the exterior, and the black disks for the interior. The arrangement below is not satisfactory because they must use the same number of each color.

The members tried many different ways to arrange the disks without success. Can you help them by finding the dimensions of a rectangular placement that would use an equal number of black and white disks? Can you find more than one configuration that would work?

What about shapes other than rectangles that might make decent placemats while using the same number of black and white disks?