A zero-sum tiling game. A plurality of "domino-like" game pieces include indicia viewable on the top surfaces of the game pieces that correspond to one, or the other, or both of two halves of the game pieces. The indicia forms a binary set. The indicia associated with one half of the game piece may be summed to indicate the value for that type of indicia for that one half of the game piece, while the indicia may more generally be "added" or "summed" overall to obtain an overall value for any desired number of halves. Particularly, it is an object of the game to lay down game pieces in such a way that each piece that is laid down completes a square that consists of four halves, wherein the sum of the indicia for the four halves is zero.