Figure 5: Sample solvable boards with an assortment of symmetry types. English peg solitare is a puzzle where the board has the form of a cross. The single field in the middle of the board is empty. Table 2: A count of solvable board positions for the various symmetry types. 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 (the programs can also display solutions). We note that for a particular board and number of pegs n, 32 movable pegs (+) are arranged on the following board such that only the middle position is empty (-). There is sometimes a unique board position with as many jumps as possible and one winning jump. This indicates there are no n-peg board positions with a unique winning jump. 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 means that in some sense these puzzles exist independently of any particular board. I am writing an assignment in java for my data structures course. 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). It is to find a solution to a peg solitaire board by using backtracking recursion. I thought I have a good solution in the works through saving the states of the board in stacks and then popping the board back when I need to go backwards. Similarly, in going from the French board to an infinite board, Two-dimensional peg solitaire There are several popular versions of two-dimensional peg solitaire. A very simple one is an extension of our previous puzzle. Searching for all n-peg symmetric or unique winning jump puzzles We would expect additional problems solvable only on a sufficiently large board. A classic game for your mobile phone On a board with 32 pegs you have to move the pegs that at the end only one peg remains in the middle of the board. On an infinite board is an interesting computational challenge. Beasley, The Ins and Outs of Peg Solitaire, Oxford Univ. Brainteaser 1: Peg Solitaire is played on a board, which in its most usual version has the shape of a cross and 33 holes, with the central hole empty and the remaining holes occupied by pins or pegs. Guy, Purging pegs properly, in Winning Ways for Your Mathematical Plays,Ģnd ed., Vol. The aim is to leave only one peg occupying the centre position. Gardner, Peg Solitaire, in Knots and Borromean Rings, Rep-Tiles and Eight Queens, To do this, the player must eliminate pegs one by one by jumping them over one. Solution to the 32 peg solitaire how to#īell, Triangular peg solitaire unlimited, Games and Puzzles J.
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