Unshackle games on 2m × (2n + 1) Grid graphs, Ladder graphs and Ladder-like graphs
Thitiphut Leelathanakitsmile_suthi@hotmail.comDepartment of Mathematics and Computer ScienceFaculty of ScienceChulalongkorn UniversityBangkok, 10330, ThailandView full profile → , *Ratinan BoonklurbCorresponding authorratinan.b@chula.ac.thDepartment of Mathematics and Computer ScienceFaculty of ScienceChulalongkorn UniversityBangkok, 10330, ThailandView full profile → , Sirirat Singhunsin_sirirat@ru.ac.thDepartment of MathematicsFaculty of ScienceRamkhamhaeng UniversityBangkok, 10240, ThailandView full profile →
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- Received:
- 01 Jan 2026
- Published Online:
- 17 Jul 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2771
- Pages:
- 2905–2938
Abstract
The Unshackle game is a combinatorial game for two players that starts with prisoners and shackles on a board such that each shackle has two ends, and each end is shackled to one prisoner. Two players alternately take turns by destroying a shackle on the board until all shackles have been destroyed. A prisoner is free when all shackles that are shackled to him are destroyed, and the player who frees the most prisoners wins and the other loses. Both players draw if neither of them can win. The prisoners and the shackles on the board can be considered as vertices and edges of a graph. This article determines the outcomes of the Unshackle games on 2m × (2n + 1) grid graphs by constructing a winning strategy for the second player, and determines the outcomes of the Unshackle games on ladder graphs and on ladder-like graphs by using mathematical induction.
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References
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