Domino questions

[David Wilson]

1. On an n x n (m x n) checkerboard, what is the smallest number of dominoes that can be placed so that no further dominoes can be placed?

2. Suppose two players, A and B, alternately place dominoes on an n x n (m x n) checkerboard until no further play is possible. A plays to maximize the final number of dominoes on the board, B to minimize. What is the number of dominoes on the board at the end of the game if A moves first? If B moves first?
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