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A complete solution for the partisan chocolate game
- Publication Year :
- 2023
-
Abstract
- The class of Poset Take-Away games includes many interesting and difficult games. Playing on an $n$-dimensional positive quadrant (the origin being the bottom of the poset) gives rise to nim, wythoff's nim and chomp. These are impartial games. We introduce a partisan game motivated by chomp and the recent chocolate-bar version. Our game is played on a chocolate bar with alternately flavored pieces (or a checkerboard). We solve this game by showing it is equivalent to blue-red hackenbush strings. This equivalence proves that the values of game are numbers and it gives an algorithm for optimal play when there is more than one chocolate bar. The checkerboard interpretation leads to many natural questions.<br />Comment: 21 pages, 9 figures
- Subjects :
- Mathematics - Combinatorics
91A46, 91A05, 91A80
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2310.13559
- Document Type :
- Working Paper