Domino questions

[franktaw at netscape.net]

From: davidwwilson at comcast.net
>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?

This might be ceiling(n^2/3), A008810.  Can someone please
check the reference there: "J. H. Conway and R. K. Guy, The Book
of Numbers, Copernicus Press, NY, 1996, number of red blocks in
Fig 2.5."
 
>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?

You don't want much, do you?

(Note for anyone who may be confused - that comment means that
I think this is likely to be a hard problem.)

Franklin T. Adams-Watters
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