Solitaire - Solution and Notation

Solitaire is based on the simple game played with pegs in a board (known as Solitaire in Great Britain and Peg Solitaire in the United States). The initial hole and peg layout (33 holes and 32 pegs) is known as the English layout (the European layout has more holes and pegs).  Starting with the initial layout, as follows,

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

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.

Solution and Notation

A solution to the 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.

  B C D F G H J  
A  
E  
I  
O  
U  
W  
Y  

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.