We define an infinite class of 2-pile subtraction games, where the amount that can be subtracted from both piles simultaneously, is a function f of the size of the piles. Wythoff's game is a special case. For each game, the 2nd player winning positions are a pair of complementary sequences, some of which are related to well-known sequences, but most are new. The main result is a theorem giving necessary and sufficient conditions on f so that the sequences are 2nd player winning positions. Sample games are presented, strategy complexity questions are discussed, and possible further studies are indicated. © 2004 by Springer Science+Business Media New York.
CITATION STYLE
Fraenkel, A. S. (2004). New games related to old and new sequences. In IFIP Advances in Information and Communication Technology (Vol. 135, pp. 367–382). Springer New York LLC. https://doi.org/10.1007/978-0-387-35706-5_24
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