Domino questions

[Richard Guy]

1.  Checked!  Unfortunately, in the printing,
red and orange are barely distinguishable.   R.

On Wed, 15 Nov 2006, franktaw at netscape.net wrote:

> 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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