publication . Preprint . 2017

Impartial Triangular Chocolate Bar Games

Miyadera, Ryohei; Nakamura, Shunsuke; Fukui, Masanori;
Open Access English
  • Published: 14 Nov 2017
Abstract
Chocolate bar games are variants of the game of Nim in which the goal is to leave your opponent with the single bitter part of the chocolate bar. The rectangular chocolate bar game is a thinly disguised form of classical multi-heap Nim. In this work, we investigate the mathematical structure of triangular chocolate bar games in which the triangular chocolate bar can be cut in three directions. In the triangular chocolate bar game, a position is a $\mathcal{P}$-position if and only if $x \oplus y \oplus z = 0$, where the numbers $x,y,z$ stand for the maximum number of times that the chocolate bar can be cut in each direction. Moreover, the Grundy number of a posi...
Subjects
free text keywords: Mathematics - Combinatorics
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