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Math Help - Classic Peg-Jumping Puzzle

  1. #1
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    Classic Peg-Jumping Puzzle

    A Classic Peg-Jumping Puzzle


    There are four red pegs and four blue pegs as shown below.
    There is an empty "hole" in the center.

    Object: switch the positions of the red and blue pegs.


    \begin{array}{ccccccccc}<br />
{\color{red}\boxed{\;}} & {\color{red}\boxed{\;}} & {\color{red}\boxed{\;}} & {\color{red}\boxed{\;}} & _{\_\_\_} & {\color{blue}\boxed{\;}} & {\color{blue}\boxed{\;}} & {\color{blue}\boxed{\;}} & {\color{blue}\boxed{\;} }\end{array}


    A peg can move into an adjacent hole
    or jump a peg of opposite color.

    Red pegs must move to the right.
    Blue pegs must move to the left.


    Good Luck!

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  2. #2
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    Solution

    Solution


    \begin{array}{ccccccccc}\\<br />
{\color{red}\boxed{\;}} & {\color{red}\boxed{\;}} & {\color{red}\boxed{\;}} & {\color{red}\boxed{\;}} & _{\_\_\_} & {\color{blue}\boxed{\;}} & {\color{blue}\boxed{\;}} & {\color{blue}\boxed{\;}} & {\color{blue}\boxed{\;} } \\ 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9\\ \end{array}

    Note that the positions are numbered, not the pegs.

    In the solution, a number is given for a move.
    You will find that the peg at that position
    has exactly one legal move.


    Spoiler:

    \begin{array}{c} \text{4 - 6} \\ \text{7 - 5 - 3} \\ \text{2 - 4 - 6 - 8} \\<br />
\text{9 - 7 - 5 - 3 - 1} \\ \text{2 - 4 - 6 - 8} \\ \text{7 - 5 - 3} \\ \text{4 - 6} \\ \text{5} \end{array}



    Last edited by Soroban; April 22nd 2009 at 04:39 PM.
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  3. #3
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    Need some help

    How do you solve this?

    Quote Originally Posted by Soroban View Post
    A Classic Peg-Jumping Puzzle


    There are four red pegs and four blue pegs as shown below.
    There is an empty "hole" in the center.

    Object: switch the positions of the red and blue pegs.


    \begin{array}{ccccccccc}<br />
{\color{red}\boxed{\;}} & {\color{red}\boxed{\;}} & {\color{red}\boxed{\;}} & {\color{red}\boxed{\;}} & _{\_\_\_} & {\color{blue}\boxed{\;}} & {\color{blue}\boxed{\;}} & {\color{blue}\boxed{\;}} & {\color{blue}\boxed{\;} }\end{array}


    A peg can move into an adjacent hole
    or jump a peg of opposite color.

    Red pegs must move to the right.
    Blue pegs must move to the left.


    Good Luck!

    Follow Math Help Forum on Facebook and Google+

  4. #4
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    Thank you very much.
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