All the Winning Bites for a by b Chomp for a and b up to 14 and Two Computational Challenges

By Shalosh B. Ekhad and Doron Zeilberger

.txt   [only .txt format]

Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger

First Written: Aug. 11, 2018

Dedicated to Richard K. Guy (b. Sept. 30, 1916) on his forthcoming 102th birthday.

In the classic book, Winning Ways, by Berlekamp, Conway, and Guy they briefly (volume 2, Chapter 18, pp. 598-599) they briefly mention the game of Chomp, and present a table of the winning bites for small boards. Here we extend their table to boards with length and width up to 14, and present two computational challenges, that would make the OEIS 500 and 100 dollars richer, respectively.

Acknowledgment: This short article was inspired by Purui Zhang and Lu Yan who just found an intriguing extension to Multiplayer CHOMP . Purui Zhang and Lu Yan are entering freshmen(!) from Fudan and Tsinguha Universities, respectively.

# Maple package

• CHOMP.txt, a Maple package to compute winnning moves for Chomp positions.

# Sample Input and Output for CHOMP.txt

• If you want to see an extension of the Table in Figure 9 of Winning Ways II (p. 599), listing all the Winning Bites for a by b chomp with a,b up to 14 (in OUR notation, consistent with matrix notation)

the input file generates the output file.

• If you want to see an extension of the Table in Figure 9 of Winning Ways II (p. 599), listing all the Winning Bites for a by b chomp with a,b up to 14 (in the Winning Way's notation)

the input file generates the output file.

Personal Journal of Shalosh B. Ekhad and Doron Zeilberger