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Math Help - checkers puzzle

  1. #1
    Junior Member samsum's Avatar
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    checkers puzzle

    Ten checkers numbered 1 – 10 are lined up as shown in the figure below. Your objective is to create five piles of two checkers each in only five moves. On each move a single checker must “jump” exactly two checkers (in either direction) and land on the next single checker. The two jumped checkers may be two single checkers side-by-side or a stacked pair.


    Hints:

    Try to use 10 pennies represent checker 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

    examples: checker 1 was on top checkers 3 and so on.....

    Have fun with it.


    I think this will help you to solve it, thanks for interested in.
    Attached Thumbnails Attached Thumbnails checkers puzzle-checker.gif  
    Last edited by samsum; September 15th 2006 at 08:23 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by samsum View Post
    Ten checkers numbered 1 – 10 are lined up as shown in the figure below. Your objective is to create five piles of two checkers each in only five moves. On each move a single checker must “jump” exactly two checkers (in either direction) and land on the next single checker. The two jumped checkers may be two single checkers side-by-side or a stacked pair.


    Hints:

    Try to use 10 pennies represent checker 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

    examples: checker 1 was on top checkers 3 and so on.....

    Have fun with it.
    A bit difficult without the figure.

    You can upload the figure using the Manage Attachments dialogue on
    the edit window (choose the advanced editing option and scroll down)

    RonL
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  3. #3
    Junior Member samsum's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    A bit difficult without the figure.

    You can upload the figure using the Manage Attachments dialogue on
    the edit window (choose the advanced editing option and scroll down)

    RonL
    yeah, it is so difficult to figure out how to solve it. If is easy, it won't be a puzzle.
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  4. #4
    dan
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    i can't even understand the problem...
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by samsum View Post
    yeah, it is so difficult to figure out how to solve it. If is easy, it won't be a puzzle.
    Don't quote me, in order to make some point not related
    to my post.

    RonL
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by samsum View Post
    yeah, it is so difficult to figure out how to solve it. If is easy, it won't be a puzzle.
    and will you cut us in on the prize if we solve this for you?

    RonL
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  7. #7
    Grand Panjandrum
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    I will unlock this thread on the 1st of October (assuming I remember), and
    if there are no correct solutions within 24 hours I will post one of the solutions.

    Gratis clue: the gaps left by checkers that have jumped are not significant
    and are to be treated as though they are not there.

    RonL
    Last edited by CaptainBlack; September 21st 2006 at 08:40 AM.
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  8. #8
    Grand Panjandrum
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    I have reopened this early as I may not be around to do this
    when I said I would.

    This is a variant of the eight coins problem.

    1. Start by jumping checker 7 over 8 and 9 onto 10.

    Now we are left with an eight checker problem with checkers 1, 2, 3, 4,
    5, 6, 8, 9
    .
    2. jump 4 over 5&6 onto 8
    3. jump 6 over 5&3 onto 2
    4. jump 3 over stack with 6&2 onto 1
    5. jump 5 over stack with 4&8 onto 9.

    (note the gaps between checkers left by jumps are ignored for subsequent
    moves)

    This generalises to any even number of checkers >=8. It is fairly easy
    to show that there is no solution for 6 or fewer checker.

    RonL
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  9. #9
    Junior Member samsum's Avatar
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    Is that so simple ?

    my solution is:

    step 1: let checker 7 jumps over 8 & 9 onto 10
    1 , 2, 3, 4, 5, 6, 8, 9, 7/10
    step2: jump checker 5 over 3 & 4 onto 2
    1, 5/2, 3, 4, 6, 8, 9, 7/10
    step 3: jump 3 over 4 & 6 onto 8
    1, 5/2, 4, 6, 3/8, 9, 7/10
    step 4: jump 9 over 3/8 onto 6
    1, 5/2, 4, 9/6, 3/8, 7/10
    step 5: the last move will jump the checker 1 over 5/2 onto 4.

    I hope this will be the same as yours. No arguments huh ? Let's others opinions. Thanks anyways Captainblack.
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