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Abstract

Wythoff's game is a kind of 2-pile Nim game, which admits taking the same number of stones from both piles. It differs only a little from the 2-pile Nim game, but their winning strategies are quite different from each other. Amazingly the winning strategy of Wythoff's game is directly related to a real number, specifically the golden ratio. In this paper we add two restrictions to this game, and investigate the winning strategy of the revised game.

Author Bio

Ryoma Aoki is now a student at Hyogo Prefectural Akashi Kita Senior High School. He wishes to major in mathematics at Tokyo University. He has much talent for mathematics, and he produced remarkable results. His dream is to be a mathematician, and he shows deep interest in the Riemann hypothesis.

Junpei Sawada is now a student at Hyogo Prefectural Akashi Kita Senior High School. He played a central role in this research. He belongs to a track and field club. He is successful in both study and club activities.

Yuki Miyake is now a student at Hyogo Prefectural Akashi Kita Senior High School. In this research, he investigated many examples and conjectured the main result. He is interested in programmings. He often participates in Olympiad in Informatics.

Hiroaki Fujiwara is now a student at Hyogo Prefectural Akashi Kita Senior High School. He motivated Aoki, Sawada and Miyake to this research. He loves mathematics, astronomy and programmings.

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