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Publication Date:
07 05 2009
DOI:
10.1515/INTEG.2009.003

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Editor-in-Chief: Nathanson, Melvyn B. / Nešetril, Jaroslav / Pomerance, Carl

6 Issues per year

Mathematical Citation Quotient 2010: 0.20

The Shortest Game of Chinese Checkers and Related Problems

Bell, George I. 1

1Tech-X Corporation, 5621 Arapahoe Ave Suite A, Boulder, CO 80303, USA. E-mail:

Citation Information: Integers. Volume 9, Issue 1, Pages 17–39, ISSN (Print) 1867-0652, DOI: 10.1515/INTEG.2009.003, May 2009

Publication History:

Received: 04/03/2008;
Accepted: 20/12/2008;
Published Online: 05/03/2012

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.

Keywords.: Chinese checkers; halma; peg jumping puzzle; peg solitaire; optimal leapfrogging

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