Three-Rowed CHOMP

By Doron Zeilberger

.pdf   .ps   .tex
Appeared in Adv. Applied Math. v. 26 (2001), 168-179.

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 .

That appeared in the `Future of Mathematics' book published by the AMS.

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 June 3, 2003: Se also a sequel to this paper, Chomp, Recurrences, and Chaos(?)

Added Aug. 27, 2018: Purui Zhang and Lu Yan just found an intriguing extension: Multiplayer CHOMP

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.

Added Jan. 30, 2019: Aviezri Fraenkel kindly pointed out a misprint in the original (and published) version. This has been corrected.

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