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:
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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