The impartial game Cram is played on a board of \(m \times n\) squares, where players alternately place a domino on the board which covers two adjacent squares that are free (not yet occupied by a domino), vertically or horizontally. The first player who cannot place a domino any more loses. Example play for a \(2 \times 3\) board:

(a) Who will win in \(3 \times 3\) Cram?

(b) Who will win in \(m \times n\) Cram when both \(m\) and \(n\) are even? (That player has a simple and precisely definable winning strategy which you have to find.)

(c) Who will win in \(m \times n\) Cram when \(m\) is odd and \(n\) is even? (Easy with (b).)
Note (not a question): Because of the known answers from (b) and (c), this game is more interesting for "real play" on an \(m \times n\) board where both \(m\) and \(n\) are odd. Play it with your friends on a \(5 \times 5\) board, for example. The situation often decomposes into independent parts, like contiguous fields of 2, 3, 4, 5, 6 squares, that have a known winner, which may help you analyse the situation.

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