July 2009 Variant Chess 61 Page 109
king than the 1926 rules, while there Taming The was no analogue of the unicorn and balloon at all. The knight was Slippery King replaced by a “centaura” which moved like a knight on a board and like a A fundamental difficulty in multi- queen between them. But it was now dimensional chess is that of confining impossible for K + Q to force mate and mating the king. Joe Joyce’s four- against a bare king, and even Parton’s dimensional Hyperchess [Joyce] uses suggested restriction of the kings a method which appears to be novel. to boards B1 and B3 didn’t help. The first reference in the literature Presumably in compensation, Parton to four-dimensional chess appears to stated that perpetual check could be have been in a paper by Dawson in claimed as a win. the December 1926 issue of the Joe Joyce’s approach is basically Chess Amateur. This presented three that of Parton, though with a 4x4 array problems, one on a 3x3x3x3 board of boards and many differences of and the other two on a 4x4x4x4, and detail. “Diagonals are evil,” he writes. employed the natural analogues of “The only way to make the game two-dimensional rules: the rook playable was to dump most of them.” moved in one dimension, the bishop It has to be said that an unfortunate simultaneously in two, a “unicorn” error in the 1926 paper bears him in three, and a “balloon” in four. out, one of the problems being The queen moved as R+Bi+U+Ba, meaningless because the Black king is the king similarly but one step only. already standing in check from a No initial array was specified and the unicorn. Not only was this overlooked variant seems never to have become by Dawson, but Anthony Dickins more than a vehicle for these three appears not to have noticed it when problems, but in principle it would quoting the problem in A Guide to appear to have been playable. In Fairy Chess (1967/69). particular, K + Q v K was a win, so To control the king and make mate there was a reasonable chance of possible, Joe introduces the idea of a converting a modest middle-game “held king”: when a player moves his advantage into a win by playing for king to the same 4x4 board as is the ending and promoting a pawn. already occupied by his opponent’s (If king and queen are allowed to king, his opponent’s king (though not move in any number of dimensions his own) is “held” and cannot leave simultaneously, K + Q v K is a win on that board. If his own king leaves the a board of size up to 5x5x5x... in any board and his opponent’s king follows number of dimensions. The stronger it to its new board, it is now his own side simply moves its king to the king which is “held”. central cell, and lets the queen do the There are many other differences rest. However, mating a king other from Parton’s game and indeed from than by pushing it to a side face and what happens in normal chess, and plonking a guarded queen directly in although these differences may seem front of it is almost impossible.) rather arbitrary they were apparently Parton, in his Sphinx Chess inspired by practical experience. (Chessical Cubism, 1971), adopted a In particular, the bishop can make a different approach. He set up a 3x3 one-step rook move to change colour, array of 4x4 boards, and a piece was the knight slides two-and-one without allowed to move either within a board jumping, and the pawn is allowed a or to the same square on another sideways move and captures with its board. So, supposing the boards to be normal move. The full rules can be numbered from A1 to C3, a bishop on found on the Chess Variants web site square c4 on board A1 could move to