Put-Together - Bill's Checkerbox

Bill's Checkerbox
Designer:Bill Cutler
Craftsman:Tom Lensch
Material:Mahogany & Holly

There is only one way the twelve pentomino pieces can be put into the 3x4x5 rectangular box with a checkerboard pattern showing on all six sides. If you count the colors of the cubes, you find there are thirty-one of one color and twenty-nine of the other. How is this possible? This is no puzzle, it's a nightmare!