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A game or puzzle comprising a plurality of polyomino pieces, each piece having on opposite faces one or more squares, said squares on each said piece and on opposite faces having markings wherein such said markings of said squares in total on both faces of said pieces comprise four or more different markings such that the pieces are capable of being assembled using their obverse faces only into a first set of one pattern comprising squares with the markings of the squares on the obverse faces of the assembled pieces forming a checkerboard pattern of two alternating markings which may be used for playing a checkers or chess type game, and the pieces may be further assembled into a second set of one or more patterns using the reverse faces of some of the pieces and the obverse faces of the remaining pieces, each pattern in the second set comprising squares forming a further checkerboard pattern of four or more markings, one of said markings being in an alternating checkerboard pattern with the remaining markings; the pieces may be further assembled into a third set of patterns using the reverse faces only of the pieces such that each pattern in the third set comprises thee different markings on the reverse side which can be arranged into a pattern such that one of the markings forms a checkerboard pattern with the other two markings; and wherein the assembly of pieces forming the first set of patterns is different from the assembly required of pieces forming the second set of patterns.