On Variations of Nim and Chomp
June Ahn, Benjamin Chen, Richard Chen, Ezra Erives, Jeremy Fleming,, Michael Gerovitch, Tejas Gopalakrishna, Tanya Khovanova, Neil Malur, Nastia, Polina, Poonam Sahoo
TL;DR
This paper introduces Monotonic Nim and Diet Chomp, two novel variations of classic combinatorial games Nim and Chomp, exploring their rules and potential strategic implications.
Contribution
It defines and analyzes two new game variants, expanding the understanding of Nim and Chomp dynamics with non-decreasing positions and move limitations.
Findings
Monotonic Nim involves non-decreasing position sequences.
Diet Chomp limits total squares removed, affecting game strategy.
The paper provides initial analysis of these variations.
Abstract
We study two variations of Nim and Chomp which we call Monotonic Nim and Diet Chomp. In Monotonic Nim the moves are the same as in Nim, but the positions are non-decreasing numbers as in Chomp. Diet-Chomp is a variation of Chomp, where the total number of squares removed is limited.
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Taxonomy
TopicsMathematics and Applications · History and Theory of Mathematics · Mathematical Dynamics and Fractals