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The Shortest Game of Chinese Checkers and Related Problems
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George I. Bell
Published/Copyright:
May 7, 2009
Abstract
In 1979, David Fabian found a complete game of two-person Chinese Checkers in 30 moves (15 by each player). This solution requires that the two players cooperate to generate a win as quickly as possible for one of them. We show, using computational search techniques, that no shorter game is possible. We also consider a solitaire version of Chinese Checkers where one player attempts to move her pieces across the board in as few moves as possible. In 1971, Octave Levenspiel found a solution in 27 moves; we demonstrate that no shorter solution exists. To show optimality, we employ a variant of A* search, as well as bidirectional search.
Received: 2008-03-04
Accepted: 2008-12-20
Published Online: 2009-05-07
Published in Print: 2009-April
© de Gruyter 2009
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Keywords for this article
Chinese checkers;
halma;
peg jumping puzzle;
peg solitaire;
optimal leapfrogging
Articles in the same Issue
- On k-Imperfect Numbers
- On Universal Binary Hermitian Forms
- The Shortest Game of Chinese Checkers and Related Problems
- On Two-Point Configurations in a Random Set
- On Rapid Generation of SL2(𝔽q)
- Tiling Proofs of Some Formulas for the Pell Numbers of Odd Index
- Some new van der Waerden numbers and some van der Waerden-type numbers
- Integer Partitions into Arithmetic Progressions with an Odd Common Difference
- On Asymptotic Constants Related to Products of Bernoulli Numbers and Factorials
