![]() ![]() Bell, Solving triangular peg solitaire, J. Bell, Triangular peg solitaire unlimited, Games and Puzzles J. Gardner, Peg Solitaire, in Knots and Borromean Rings, Rep-Tiles and Eight Queens, Guy, Purging pegs properly, in Winning Ways for Your Mathematical Plays,Ģnd ed., Vol. Beasley, The Ins and Outs of Peg Solitaire, Oxford Univ. On an infinite board is an interesting computational challenge. ![]() Searching for all n-peg symmetric or unique winning jump puzzles ![]() We would expect additional problems solvable only on a sufficiently large board. Similarly, in going from the French board to an infinite board, We saw in going from the English to French board that additional puzzles were found that were solvable on theįrench board but not on the English board (Figure 5c). Triangle Peg Solitaire Instructions Jump one peg over another into an empty spot, removing the jumped peg from the board. This means that in some sense these puzzles exist independently of any particular board. Table 4: A summary of board positions with a unique winning jump by pegs and maximum starting jumps,Īny solvable board position presented above is also solvable when considered on an infinite board. This indicates there are no n-peg board positions with a unique winning jump. There is sometimes a unique board position with as many jumps as possible and one winning jump. We note that for a particular board and number of pegs n, (the programs can also display solutions). Table 4 summarizes the results of these calculations,Īnd Figures 10- 12 show example board positions calculated using this strategy.Īll of these puzzles can be played on my Javascript programs Table 2: A count of solvable board positions for the various symmetry types. Figure 5: Sample solvable boards with an assortment of symmetry types. The game is known as solitaire in Britain and as peg solitaire in the US where 'solitaire' is now the common name for patience. Some sets use marbles in a board with indentations. (the minimum value of the board code over all symmetry transformations).Ī board position is conveniently (but not efficiently) stored in a single, 64-bit integer. Peg solitaire, Solo Noble or simply Solitaire is a board game for one player involving movement of pegs on a board with holes. We do not store duplicate copies of board positions which are rotations or reflections of one another,Įach symmetric board position has a single entry, determined by the mincode() For details on how these calculations are done, see. ![]()
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