Ratwyt

Summary

WYTHOFF is played on a pair of nonnegative integers, (M, N). A move either subtracts a positive integer from precisely one of M or N such that the result remains nonnegative, or subtracts the same positive integer from both M and N such that the results remain nonnegative. The first player unable to move loses. RATWYT uses rational numbers instead, transformed using a generalization of the rules of WYTHOFF. Using the Calkin-Wilf tree, we show how to play RATWYT, and any other rational take-away game.

Additional information

Notes on contributors

Aviezri S. Fraenkel

Aviezri S. Fraenkel ([email protected]) received his Ph.D. in 1961 from UCLA. He received the Euler Medal in 2005. In 2006 he received the WEIZAC Medal from the IEEE as a member of the team who built WEIZAC, one of the first computers in the world. In 2007 his Responsa Project, an early full text retrieval system, won the Israel prize. He is affiliated with the Dept. of Computer Science and Applied Mathematics, Weizmann Institute of Science. Research interests include combinatorial games, combinatorics, and computational complexity.