Sprague (1963) considered the problem of "rolling" five cubes, each which an upright letter "A" on its top, on a chessboard. Here "rolling" means the cubes are moved from square to adjacent square by being tipped over along an edge (as one might move a heavy box) in a series of quarter turns. If five such cubes are initially arranged in the shape of a plus sign with the edges of the of plus sign aligned with the upper and left corners of a chessboard (top left in above figure), then it is impossible to obtain a straight row or column with all "A"s on top and oriented identically. The best that can be done is to place four out of the five "A"s in the same orientation and facing upward, with the remaining "A" also facing upward and rotated a quarter turn, illustrated above in the bottom row (Gardner 1984, pp. 75-78).
