On Kotzig's Nim (Q2926289)

The aim of the paper is to cast some new light on an old combinatorial game named Kotzig's Nim [\textit{A. Kotzig}, Čas. Mat. Fys. 71, 55--66 (1946; Zbl 0060.11602)]. The authors hope that this paper will lead to new results and renewed interest about this ``enticing game, for which the winning strategy (in most cases) remains an enigma.''NEWLINENEWLINEFrom the author's abstract: ``In 1946, Anton Kotzig introduced Kotzig's Nim, also known as Modular Nim. This impartial, combinatorial game is played by two players who take turns moving around a circular board; each move is chosen from a common set of allowable step sizes. We consider Kotzig's Nim with two allowable step sizes. Although Kotzig's Nim is easy to learn and has been known for many decades, very few theorems have been established. We prove a new primitive theorem about Kotzig's Nim. We also introduce a series of conjectures about periodicities in Kotzig's Nim, based on computational exploration of the game.''NEWLINENEWLINEThe paper ends with the discussion of several conjectures about primitive games.