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Choiss. Starting with a 2x2 center, players assemble a 64 square board of any shape before play.[All Comments] [Add Comment or Rating]

Joost Brugh wrote on Sun, May 21, 2006 06:33 PM UTC:

I played it a few times. I think I figured out the algorithm.

After placing the tiles, there are 12 ranks with total number of squares
64. Define: Area(n) = Number of squares on ranks 1..n. As there are 12
files, Area(1) = 0..12, Area(2) = 0..24 etc. Area(12) = 64. White may
place pieces on rank r if Area(r) is 32 or less. For Black, it works the
same, except that rank 12 is now rank 1 etc.

For example, if White and Black construct a Chessboard on ranks 2..9 (with
eight squares on each rank. Then, for White: Area(1) = 0, Area(2) = 8,
Area(3) = 16, Area(4) = 24, Area(5) = 32, Area(6) = 40 Area(n) > 40 for
n>6б, so White can place pieces on ranks up to 5. For Black the same
results in ranks from 12 down to 6.

If Area(n)=33, you just can't place pieces on the n'th rank. The maximum
number of squares on the n'th rank is 12, so Area(n-1) must be at least
21. This is enough space to drop the 16 pieces. The game, however gets
stuck if you have to drop your King into check.