New

Mind: Selection gets active after pushing the 'new' button.

Board Shape

Spoiler alert! Here are some solutions to step through:

Single vacancy to single survivor challenges

Solving English Solitaire

Here the single vacancy and single survivor are in same centered position (complement challenge)
This is the most aesthetic silver bullet solution of the English Solitaire puzzle. There are multiple solutions known to the challenge. Here I selected solutions with some symmetrical well balanced board positions. That makes the aesthetic solution easier to recall.


Solving Triangular5

On a Triangular5 board there are 4 different type of peg positions: Corner position, mid edge position, the position in between both and the position not touching any edge or corner. Each field is of one of these types and by symmetry (board axis mirroring and turning) you can see that no other field types exist. As such you can distinguish among four single vacancy to single survivor challenges. And no matter which initial position is chosen as the vacancy you can always finally end up with just one peg remaining on optimal strategy.

Minor hint: In all solutions of an Triangular5 board never start a peg's jump from any of the three inner board positions.


Solving Triangular6

There is a single vacancy to single survivor solution for each chosen possible vacancy on this Triangular6 board, too. Depending on the board situation a consecutive series of jumps with same peg could be performed. Such a series of jumps is called a sweep. A sweep can be seen as a single move removing multiple pegs. Here are some solutions shown containing such sweeps.


Solving French Solitaire

In case of the French Solitaire there is no solution to end up with a single survivor when the single vacancy is in centered position of the board. Meaning there are no solvable complement challenges. Instead the most aesthetic solutions have the vacancy off the centered position and the single survivor finally is located at the position turning the board by 180 degrees around the center.

Rules

Jump with a selected peg over an adjacent peg removing it.

The mind bending puzzle of Peg Solitaire is well-known using different board shapes and different amount of holes for placing the pegs. The common mechanics is that a selected peg is capable to jump any directly adjacent single neighbour in straight direction onto a free position. A peg is removed as it gets jumped. The selected peg will end its move just on the first free field behind the peg that gets removed then.


Supported board shapes include

  • triangular 15 peg positions (also called triangular 5),
  • triangular 21 peg positions (also called triangular 6),
  • English board with orthogonal pattern of 33 peg positions, and
  • French board with orthogonal pattern of 37 peg positions.

Due to the different shapes of the board in this implementation straight jumps are possible in either two or three directions (either four or six directions if counting forward and backward jumps separately).

In Peg Solitaire you select one of the pegs first. This peg is going to be removed building a starting position.

By jumping the total number of pegs is reduced then. All starting positions of a 15 hole and 21 hole triangular board shape do definitively allow to finally end up with just one peg remaining on optimal strategy. This class of challenges are referred to as single vacancy to single survivor challenges. Other board shapes and sizes have both, some solvable and some unsolvable, starting positions for single vacancy to single survivor, too.

If the single vacancy position matches the position of the survivor the challenge is called a complement challenge. As a tough task you might find out which board shapes and vacancies either do or do not allow a complement challenge.

Each jump reduces the total amount of remaining pegs by one. Depending on the board situation a consecutive series of jumps with same peg could be performed obviously. Such chained jumps (also called sweeps) could be seen as a single move. The question arises to find the best solutions with minimum amount of moves then.

Feel free to find all possible solutions for these different kind of challenges.

Legal

Oliver Merkel, cc-by-nc-nd 4.0.

Copyright (c) 2016, 2023
@author Oliver Merkel, Merkel(dot) Oliver(at) web(dot) de.
All rights reserved.
Logos, brands, and trademarks belong to their respective owners.

All source code also including code parts written in HMTL, Javascript, CSS is under MIT License.

The MIT License (MIT)

Copyright (c) 2016, 2023 Oliver Merkel, Merkel(dot) Oliver(at) web(dot)de

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

If not otherwise stated all graphics (independent of its format) are licensed under
Creative Commons License
Images are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Peg Solitaire Principles and Concepts

The basic concept of removing a peg by jumping over the peg in any Peg Solitaire variant belongs to the public domain due to its age and unknown creator.

Commonly used are square-shaped, cross-shaped, or any triangular Solitaire boards first referenced or dating back even centuries ago.

Anyway one might find additional expired or active claims for patents or other legal protection of related mechanics, too, like utility compartments or specific design patterns beyond the Peg Solitaire itself.

  • Billy J. Burden, 'Pegboard game unit with utility compartment', US 3658334 A, Apr. 25, 1972.
  • Homer H. Jenkins, 'Peg and hole game apparatus', US 2727745 A, Dec. 20, 1955.
  • Charles H. Rickert, 'Puzzle', US 484882 A, Patented Oct. 25, 1892.
  • Herbert M. Smith, 'Puzzle', US 462170 A, Patented Oct. 27, 1891.

Third Party Code Licenses

This Peg Solitaire implementation uses unmodified independent code libraries provided by third parties. Since their licenses might vary the corresponding information is externally linked below. Thus these external links will enable you to reproduce any copyright notice, any related list of conditions, disclaimers, and especially the copyright holders and authors of the corresponding third party functionality.

jQuery: MIT jQuery UI: MIT Snap.svg: Apache License V2.0