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Some chess variants use more than a single board per match. Bughouse chess, for example, involves four players playing two simultaneous matches on separate boards. [18] Alice Chess is a popular variant which is usually played on two boards to facilitate the movement of pieces between the boards. [19]
For instance, the n+k dragon kings problem asks to place k shogi pawns and n+k mutually nonattacking dragon kings on an n×n shogi board. [12] Nonstandard boards Pólya studied the n queens problem on a toroidal ("donut-shaped") board and showed that there is a solution on an n×n board if and only if n is not divisible by 2 or 3. [13] Domination
This is equal to the square of the number of grains on the first half of the board, plus itself. The first square of the second half alone contains one more grain than the entire first half. On the 64th square of the chessboard alone, there would be 2 63 = 9,223,372,036,854,775,808 grains, more than two billion times as many as on the first ...
If two squares of opposite colors are removed, then the remaining board can always be tiled with dominoes; this result is Gomory's theorem, [22] after mathematician Ralph E. Gomory, whose proof was published in 1973. [18] [20] Gomory's theorem can be proven using a Hamiltonian cycle of the grid graph formed by the chessboard squares. The ...
The 0x88 chess board representation is a square-centric method of representing the chess board in computer chess programs. The number 0x88 is a hexadecimal integer (136 10 , 210 8 , 10001000 2 ). The rank and file positions are each represented by a nibble (hexadecimal digit), and the bit gaps simplify a number of computations to bitwise ...
Alice Chess – played with two boards, one of which starts empty. After the completion of each move, the piece that moved is transferred to the same square of the other board (after a move on the second board, the piece returns to the first board). Hexagonal chess – any of various variants played on a hexagonal board or board with hexagonal ...
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