One-Dimensional Peg Solitaire, and Duotaire
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 $\cal P$-positions nor the $\cal N$-positions (i.e. wins for the previous or next player) are described by a regular or context-free language.
To our knowledge, this item is not available for
download. To find whether it is available, there are three
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.
|Date of creation:||Sep 2000|
|Contact details of provider:|| Postal: 1399 Hyde Park Road, Santa Fe, New Mexico 87501|
Web page: http://www.santafe.edu/sfi/publications/working-papers.html
More information through EDIRC
When requesting a correction, please mention this item's handle: RePEc:wop:safiwp:00-09-050. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Thomas Krichel)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.