Steve Byrnes <sbyrnes321@yahoo.com>

07/31/02 05:28 PM

       
        To:        tony.sun@vftis.spx.com
        cc:        
        Subject:        Chomp results



Dear Mr. Sun:

Having read your interesting paper "The Sprague-Grundy
function for Chomp", I want to inform you that I
proved the conjecture you suggest in it (that, if the
bottom (n-1) rows of an n-row chomp game are fixed,
the difference between the top row length and the
Sprague-Grundy value is eventually periodic), as part
of my research project at the Research Science
Institute, a high-school summer research program at
MIT. You can read my end-of-the-summer paper at:

web.mit.edu/byrnes/www/main.pdf

I should apologize for a few things. First, there are
probably typos and things that could be explained
better, since it was written for a deadline. Second, I
use some non-standard notation: e.g. "losing position"
for P-position and "winning position" for N-position;
"nim-value" instead of Sprague-Grundy function; and I
put the poisoned square in the bottom-left instead of
the top-left). I would have gone through and changed
all of it, but, again, I was writing for a deadline.
As it turned out, I didn't come across your paper
until most of the way through the summer, so some of
the results I initially got were already in your paper
(I included them in the end-of-the-summer paper
anyway, citing you). Anyway, I'll probably fix up the
paper, cut out the already-proven stuff, then use it
for an Intel Science Talent Search project. I would
love to hear any information about Chomp results
relevant to this paper, or any comments in general.
Thank you very much for your time.

Sincerely,
Steve Byrnes

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