One-Dimensional Peg Solitaire, and Duotaire

Details One-Dimensional Peg Solitaire, and Duotaire One-Dimensional Peg Solitaire, and Duotaire

2000-08-22

arxiv.org/abs/math/0008172v1

More Games of No Chance, MSRI Publications 42, 2002, pp. 341-350

Mathematics

Combinatorics

Partlt presented at the 2000 MSRI Workshop on Combinatorial Games

Scientific paper

We solve the problem of one-dimensional Peg Solitaire. In particular, we show that the set of configurations that can be reduced to a single peg forms a regular language, and that a linear-time algorithm exists for reducing any configuration to the minimum number of pegs. We then look at the impartial two-player game, proposed by Ravikumar, where two players take turns making peg moves, and whichever player is left without a move loses. We calculate some simple nim-values and discuss when the game separates into a disjunctive sum of smaller games. In the version where a series of hops can be made in a single move, we show that neither the P-positions nor the N-positions (i.e. wins for the previous or next player) are described by a regular or context-free language.

Affiliated with

Also associated with

No associations

Rating

One-Dimensional Peg Solitaire, and Duotaire does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with One-Dimensional Peg Solitaire, and Duotaire, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and One-Dimensional Peg Solitaire, and Duotaire will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-134234