Domineering

A two-player game, also called crosscram, in which player has horizontal dominoes and player has vertical dominoes. The two players alternately place a domino on a board until the other cannot move, in which case the player having made the last move wins (Gardner 1974, Lachmann et al. 2000). Depending on the dimensions of the board, the winner will be , , 1 (the player making the first move), or 2 (the player making the second move). For example, the board is a win for the first player.

Berlekamp (1988) solved the general problem for board for odd . Solutions for the board are summarized in the following table, with a win for for .

	win		win		win
0	2	10	1	20	H
1	V	11	1	21	H
2	1	12	H	22	H
3	1	13	2	23	1
4	H	14	1	24	H
5	V	15	1	25	H
6	1	16	H	26	H
7	1	17	H	27	1
8	H	18	1	28	H
9	V	19	1	29	H

Lachmann et al. (2000) have solved the game for widths of , 3, 4, 5, 7, 9, and 11, obtaining the results summarized in the following table for , 1, ....

	winner
3	2, V, 1, 1, H, H, ...
4	H for even and all
5	2, V, H, V, H, 2, H, H, ...
7	H for
9	H for
11	H for

Bullock created a program called Obsequi that solved the additional cases , , , , and .