Quarto! has a 4×4 board and 16 pieces. Each
piece has four dichotomous attributes – color, height, shape, and
consistency – so each piece is either black or white, tall or short,
square or round, and hollow or solid. The object is to place the fourth
piece in a row in which all four pieces have at least one attribute in
common. The twist is that your opponent gets to choose the piece you
place on the board each turn.