What is European Peg Solitaire?
European Peg Solitaire, also called French solitaire, is played on a board of 37 holes. It is the English cross of 33 holes with one more hole in each of the four inner corners between the arms, which gives the board an almost round, octagonal outline.
The moves are the same as on the English board: a peg jumps over a neighbouring peg, along a row or a column, into the empty hole beyond, and the jumped peg is removed. You win by leaving a single peg.
With the centre hole empty this board cannot be solved, whatever you do. Here the game starts with c1 empty instead (columns a to g from the left, rows 1 to 7 from the top), the left hole of the top row, and from there the board can be cleared down to one peg. That last peg can only end on e1, b4, e4 or e7.
Rule changes
| Rule | Standard Peg Solitaire | European Peg Solitaire |
|---|---|---|
| Board | Standard Peg Solitaire33 holes in a cross: arms three holes wide and two long around a 3×3 centre. | European Peg Solitaire37 holes: the same cross plus one hole in each inner corner between the arms. |
| Empty hole at the start | Standard Peg SolitaireThe centre hole, with 32 pegs on the board. | European Peg Solitairec1, the left hole of the top row, with 36 pegs on the board. The centre start cannot be solved on this board. |
| Where the last peg can end | Standard Peg SolitaireOnly in the centre (d4) or in the middle hole of an arm's outer edge (d1, a4, g4, d7). | European Peg SolitaireOnly on e1, b4, e4 or e7. |
| Jumps in a solution | Standard Peg Solitaire31. | European Peg Solitaire35. |
| Finish in the starting hole | Standard Peg SolitaireOffered as an option: the last peg must end in the centre. | European Peg SolitaireNot offered: on this board the last peg can never end in the hole that was empty at the start, from any start. |
History
The earliest records of the game come from France at the end of the 17th century: an engraving by Claude Auguste Berey shows Anne de Rohan-Chabot, Princess of Soubise, with a solitaire board, and the French magazine Mercure galant described the board, its rules and problems to solve on it. The 37-hole board is the French form of the game and is still known as the French or European board.
That the centre start has no solution on this board follows from a counting argument known as position classes, set out by N. G. de Bruijn in 1972 and in Winning Ways for your Mathematical Plays by Elwyn Berlekamp, John Conway and Richard Guy (1982). Problems on this board therefore start with another hole empty, such as the c1 start used here.