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Interesting: Alice chess is not 3-dimensional, but it's moving between several 2-dimensional worlds. So, what about game, where pieces moves between many 0-dimensional worlds (0-dimensional board have only 1 square)? For example, there are several groups of these 'worlds' (cells), each group have certain color. Say, piece A moves from red squares to blue and green suares, from blue squares to purple and yellow squares, and so on, piece B, for example, from red squares moves to yellow, orange and green squares if no more than half of blue squares or no less than half of brown squares are occuppied, and so on? What do you think?