Peg Solitaire

Making moves

The objective is to end up with just one peg remaining on the board, in the central hole, by making legitimate moves (jumping horizontally or vertically over a single peg into a vacant hole, and removing the jumped-over peg - see Legitimate moves below for full details).

On a touch screen, the best way to move a peg is to slide it in the direction of the empty hole you wish it to end up in. If the move is legitimate, the peg will be moved and the jumped-over peg will be removed.

If your screen is not a touch screen, or if you prefer just to tap rather than slide, just tap the peg to be moved.

If the peg can legitimately be moved, and there is only one hole that it can be moved to, it will be repositioned and the peg jumped over will be removed.

If the peg can legitimately be moved, but there are two or more possible destinations for the peg to go to, the peg itself will be highlighted and the possible destination holes will be shown with question marks on them. You then have to select the desired destination by tapping the destination hole. So, given the following situation

you could tap any of the three holes with question marks on them. Selecting the left one would result in the following layout:

Note: once the system is waiting for you to choose the destination, you cannot then slide the peg: you must complete the move by tapping the destination.

If you tap a peg that can't be moved, nothing happens.

If you make a wrong move and wish to rewind the move, simply press the Undo button. The pegs will be moved back to their original positions. You can press this button any number of times consecutively - and even rewind back to the starting layout.

Solve facility

If you are unable to solve the puzzle, you can press the Solve button. This shows you the solution, step-by-step, with each peg to be moved shown highlighted before the move takes place. Note: once you have selected this facility, the rewind facility is no longer available until a new puzzle is started.

The solution shown for the full layout is as described below in Solution and Notation.

Peg Solitaire

This application is based on the puzzle played with pegs in a board (known as Solitaire in Britain and Peg Solitaire in the United States). In the classic 'English layout' puzzle, the board has 33 holes and 32 pegs, with the central hole empty.

The objective is to end up with just one peg on the board in the central hole that started off empty, by making a series of simple 'jump and take' moves.

In this application, in addition to the classic full layout, many different starting layouts can be generated for you by the system - still with the objective of ending up with one peg in the middle. A reduced number of pegs in the starting layout not only makes the puzzle quicker to solve but also makes the puzzle a lot easier - and the full puzzle is undoubtedly very difficult.

Legitimate moves

A legitimate move comprises taking a peg and moving it over an occupied hole (with a peg) into an empty hole, moving vertically or horizontally (diagonal moves are not allowed). The peg that has been jumped over is removed from the board.

So, for the classic full layout we might move any of the highlighted pegs into the centre hole as our first simple move.

Moving the top one would result in a layout as follows:

The objective is to make a series of legitimate moves that result in just one peg remaining on the board, in the central square.

Exiting

Tap the device back twice to exit the application. The current state is remembered so that you continue when you open it up again.

Solution and Notation

A solution to the full puzzle was found by Ernest Bergholt in 1912. This solution is presented below together with a way of helping you to remember how to solve it. In order to help you memorize the solution, we introduce notation devised by David Wolstenholme.

The rows of the board are labelled top-to-bottom with the 5 vowels of the English alphabet, together with the 2 letters that sometimes take the place of a vowel, namely W (the W has a long U or OO sound in 'NEW') and Y (as in 'SKY' or 'HAPPY'); these seven are also the seven vowels of the Welsh language. The columns are labelled left-to-right with the first seven consonants of the English alphabet from B through to J. These are shown on the main playing board. A particular hole is referred to by its column letter followed by its row letter. So, the central hole is referred to as FO.

A simple 'jump and take' move is specified by the reference name of the starting position of the peg being moved, followed by a letter indicating the direction: R (right), L (left), U (up) or D (down). So, the first move shown in the example above would be specified as FED.

The solution to the puzzle as a set of 31 simple moves is given in the first column of the table below.

Now, this 31-step solution could not be called easy to remember. To aid memory we introduce some additional notation and some move combinations that form memorable patterns. The solution using this notation is given in the second column of the table, together with diagrams showing the order and direction of the simple moves that make up these combinations (green is first, red second). These combo moves and the associated notation are described in detail below the table.

Move combinations and notation

Single move

If, with the board layout at the time, a peg in a particular hole can be moved in only one direction, the direction part of the move specification may be omitted. So, for example, move 7 above may be specified as just GO rather than GOD.

Related moves by two different pegs

Tee move (T)

A Tee move is a combination of two simple moves by different pegs. It consists of a simple horizontal move (left or right, whichever is possible), followed by an upward move of a different peg into the empty hole formed when the peg jumped over is removed (the two moves form a T-shape as shown in the diagrams). This sequence of moves is referred to by the starting position of the first peg moved followed by the letter T. So, for example, moves 1 and 2 of the solution can be referred to as COT.

Meet-and-match move (M)

A Meet-and-match move is again a combination of two simple moves by different pegs. The first is a simple horizontal move (left or right, whichever is possible). The second is also a horizontal move, by a different peg, in the opposite direction, again into the hole formed when the peg jumped over is removed; essentially, the peg moved in the first simple move meets its match as it is removed by the peg it meets in the first move. This sequence of moves is referred to by the starting position of the first peg moved followed by the letter M. So, moves 3 and 4 of the solution can be referred to as BUM.

Cascade move (C)

A Cascade move is again a combination of two simple moves by different pegs. The first is a simple downward peg move. The second is also a downward move, by a second peg, which lands in the hole originally occupied by the first peg; that is, the peg moved in the first simple move is replaced by one from two holes above - a cascade. This sequence of moves is referred to by the starting position of the first peg moved followed by the letter C. So, moves 10 and 11 of the solution can be referred to as DIC.

Complex moves by a single peg

Side-step move (S)

A Side-step move is a combination of two simple moves by the same peg around the edge of the board in an anticlockwise (counterclockwise) direction. The first is a simple move in one direction, as appropriate, while the second is a move by the same peg, in a direction at 90 degrees to the initial direction - a side-step. This sequence of moves is referred to by the starting position of the peg moved followed by the letter S. So, moves 8 and 9 of the solution can be referred to as DYS.

Long-L move (LL)

A Long-L move is a combination of three simple moves by the same peg. The first is a simple move downwards. The second and third are two moves to the right by the same peg (these moves form the shape of a letter L, with a long base). This sequence of moves is referred to by the starting position of the peg moved followed by the letters LL. So, moves 17, 18 and 19 of the solution can be referred to as BILL.

Five move (F)

A Five move is a combination of five simple moves by the same peg. The first two moves must be in the same direction. The third move is at 90 degrees to this. The fourth move is at 90 degrees to the third move. The fifth move must be upwards. This sequence of moves (two-turn-turn-up) is referred to by the starting position of the peg moved followed by the letter F. So, moves 12, 13, 14, 15 and 16 of the solution - a U-shaped set of moves - can be referred to as GEF, while moves 26, 27, 28, 29 and 30 - a saucepan-shaped set of moves - can be referred to as CIF.

Memorizing the solution

Most of the 13 move specifications in the third column form words or names, or nearly, so become easier to remember. A way to remember the first 12 of these (the last is so simple anyway) is to think of the following little story.

Tramp gassed in hut

On a COT lies a BUM in a HUT, gasping for breath. He tries to GO but DYS (dies).

Four cops arrive to investigate: DIC (Dick), GEF (Geoff), BILL and JIM.

It's JUS' GAS, they conclude, finding a leak near a bottle of CIF.

About Peg Solitaire

This Peg Solitaire application has been designed by Dr David Wolstenholme.

This software may be used for personal purposes only. It may not be used for commercial purposes.

The software, code and script of this application may not be copied or be distributed to others.

The software, code and script may not be altered in any way.

Copyright of the software, code and script, and its help documentation, is owned by TopAccolades Limited. No part of the software, code, script or documentation may be copied or used in another application or document.

Although every effort has been made to ensure that this software functions as intended, TopAccolades Limited provides no warranty of merchantability, or fitness for a particular purpose, in relation to this application or its support.

TopAccolades Limited shall not be liable for any damages whatsoever arising out of the use of or inability to use this application or the provision of or failure to provide support.

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