A Combinatorial Approach to the Solitaire Game Journal Articles

abstract

• The classical game of peg solitaire has uncertain origins, but was certainly popular by the time of Louis XIV, and was described by Leibniz in 1710. One of the classical problems concerning peg solitaire is the feasibility issue. An early tool used to show the infeasibility of various peg games is the rule-of-three [Suremain de Missery 1841]. In the 1960s the description of the solitaire cone [Boardman and Conway] provides necessary conditions: valid inequalities over this cone, known as pagoda functions, were used to show the infeasibility of various peg games. In this paper, we recall these necessary conditions and present new developments: the lattice criterion, which generalizes the rule-of-three; and results on the strongest pagoda functions, the facets of the solitaire cone.

authors

• AVIS, David
• Deza, Antoine
• Shmuel, ONN

publication date

• April 25, 2000

has subject area

• 08 Information and Computing Sciences (FoR)
• 09 Engineering (FoR)
• Networking & Telecommunications (Science Metrix)

published in

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences  Journal

start page

• 656

end page

• 661

volume

• 83

issue

• 4