clifford_a-_pickover_surfing_through_hyperspacebookfi-org

172 appendix a
Figure A.2
Initial empty Sz'kwa board.
watch the computer do it. For more information, visit: http://www.superliminal.
com/cube, htm.
Hyperdimensiond Sz'kwa
An alien challenges you to a simple-looking, competitive game. You hold twentyfive
white crystals in your hand; the alien holds twenty-five black crystals. At the
start of the game, the circular board would have no crystals (Fig. A.2).
You and the alien take turns placing a crystal on the board at the positions with
black dots. The rules are as follows. If a player's crystal is completely surrounded by
the opponent's crystals, it is captured. Figure A.3 shows the capture of a black
piece (left) and the capture of two white pieces (right). When a player has no crystals
left to place on the circular board, or no empty sites on which to place a crystal
without its being captured, the game ends. The winner is the player who holds the
greatest number of crystals.
How many different arrangements of crystals on the playing board exist? Is it
better to be the first player? Can you write a program that learns strategies by playing
hundreds of games and observing its mistakes? Develop a multidimensional
Sz'kwa game where the center site on the Sz'kwa board connects center sites on
adjacent boards or where all sites connect to the corresponding positions on adjacent
boards. First try a game using just two connected boards and then three. Generalize
your discoveries to N boards. These versions represent hyperdimensional
Sz'kwa (Fig. A.4).