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    peg solitaire

    peg solitaire
    Also known as Hi-Q, a game that, in its commonest form, is played with 32 pegs or marbles on a rectangular grid, the middle position of which starts out empty. A peg may jump horizontally or vertically, but not diagonally, over a peg in an adjacent square into a vacant square immediately beyond. The peg that was jumped over is then removed. The object is to be left with a single peg in the center position.


         1   2   3   4   5   6   7 
     1           +   +   +         
     2           +   +   +         
     3   +   +   +   +   +   +   + 
     4   +   +   +       +   +   + 
     5   +   +   +   +   +   +   + 
     6           +   +   +         
     7           +   +   +         


    The quickest solution of Solitaire was found by Ernest Bergholt in 1912 and was proved to be minimal by John Beasley in 1964. It involves the following moves:
    1. 46 right arrow 44.
    2. 65 right arrow 45.
    3. 57 right arrow 55.
    4. 54 right arrow 56.
    5. 52 right arrow 54.
    6. 73 right arrow 53.
    7. 43 right arrow 63.
    8. 75 right arrow 73 right arrow 53.
    9. 35 right arrow 55.
    10. 15 right arrow 35.
    11. 23 right arrow 43 right arrow 63 right arrow 65 right arrow 45 right arrow 25.
    12. 37 right arrow 57 right arrow 55 right arrow 53.
    13. 31 right arrow 33.
    14. 34 right arrow 32.
    15. 51 right arrow 31 right arrow 33.
    16. 13 right arrow 15 right arrow 35.
    17. 36 right arrow 34 right arrow 32 right arrow 52 right arrow 54 right arrow 34.
    18. 24 right arrow 44.

    Reference
    1. Beasley, John D. The Ins and Outs of Peg Solitaire. New York: Oxford University Press, 1985.

    Related entry

       • mechanical puzzles


    Related categories

       • GAMES AND PUZZLES
       • MATHEMATICS



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