A game or puzzle including a plurality of polyomino pieces which have the ob verse sides and reverse sides marked with different markings, there being at least three markings in total on the obverse and re verse sides of the pieces. The pieces may be assembled u sing both sides into different arrays of eight by eight squares defining checkerb oard patterns for use in playing the game of chess or ch eckers. The pieces may also be assembled into a cube comprising four by four by four squares.