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Take-Away Games

By Zieve, Michael

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Book Id: WPLBN0000654334
Format Type: PDF eBook
File Size: 211.61 KB
Reproduction Date: 2005
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Title: Take-Away Games  
Author: Zieve, Michael
Language: English
Subject: Science., Mathematics, Logic
Publication Date:


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Zieve, M. (n.d.). Take-Away Games. Retrieved from

Mathematics document containing theorems and formulas.

Excerpt: Several works, including [Berlekamp et al. 1982; Epp and Ferguson 1980; Schwenk 1970], have studied take-away games where the players alternately remove a positive number of counters from a single pile, the player removing the last counter being the winner. On his initial move, the first player may remove any number of counters, so long as he leaves at least one. On each subsequent move, a player may remove at most f(n) counters, where n is the number of counters removed by his opponent on the preceding move. Thus, any mapping f from the positive integers to themselves defines such a take-away game.


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