Peg Jumping for Fun and Profit
| dc.creator | Bradley, David M. | |
| dc.creator | Thomas, Hugh | |
| dc.date | 2004-11-12 | |
| dc.date | 2005-04-01 | |
| dc.date.accessioned | 2026-07-07T05:14:15Z | |
| dc.date.available | 2026-07-07T05:14:15Z | |
| dc.description | We consider the problem of determining the minimum number of moves needed to solve a certain one-dimensional peg puzzle. Let N be a positive integer. The puzzle apparatus consists of a block with a single row of 2N+1 equally spaced holes which, apart from the central hole, are occupied by an equal number N of red and blue pegs. The object of the puzzle is to exchange the colors of the pegs by a succession of allowable moves. Allowable moves are of two types: a peg can be shifted from the hole it occupies into the empty hole adjacent to it, or a peg can jump over an adjacent peg into the empty hole. We exhibit a sequence of N^2+2N moves that solves the puzzle, and prove that no solution can employ fewer moves. | |
| dc.description | Original: 7 pages, recreational mathematics. Replacement: 6 pages, 6 figures, conjectured lower bound proved, retitled | |
| dc.identifier | https://arxiv.org/abs/math/0411275 | |
| dc.identifier | http://arxiv.org/abs/math/0411275 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73206 | |
| dc.subject | Combinatorics | |
| dc.subject | 00A08 (Primary); 68Q17, 97A20, 97A90, 68R15 (Secondary) | |
| dc.title | Peg Jumping for Fun and Profit | |
| dc.type | text |