By Doron Zeilberger
Written: Sept. 5, 2000.
David Gale's beautiful game of CHOMP looks `Nim-like', but it
is much harder and deeper than Nim, because it can not
be `factorized' into simple games. It has the same flavor as
enumeration problems in statistical mechanics, and is probably
equally intractable. Yet one has to do what one can,
getting help, if necessary, from our machine friends.
In addition to sketching my approach to 3-Rowed Chomp
(to really understand it, consult the source-code of the Maple package
Chomp3Rows, see the link below), there is a `two cultures' thread
throughout the article that was inspired by W.T. Gowers's fascinating
article
The Two Cultures Of Mathematics .
IMPORTANT: This article is accompanied by a Maple package
Chomp3Rows .
If you don't have Maple (shame on you!) and
you still want to see the table of losers, look at the
Table of Losers (Output of PTable(115)).
Added Aug. 27, 2018: Purui Zhang and Lu Yan just found an intriguing extension:
Multiplayer CHOMP
Added Jan. 30, 2019: Aviezri Fraenkel kindly pointed out a misprint in the original (and published) version.
This has been corrected.
Doron Zeilberger's List of Papers
.pdf
.ps
.tex
Appeared in Adv. Applied Math. v. 26 (2001), 168-179.
Added June 3, 2003: Se also a sequel to this paper,
Chomp, Recurrences, and Chaos(?)
Acknowledgement: I first heard about Chomp, many years ago (ca. 1980),
from Aviezri Fraenkel. The present paper was inspired by
interesting conversations with Yaron Raviv (Ph.D. candidate in
Economics at Princeton Univ.), who reminded me about Chomp.