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Math Help - Problem Solving

  1. #1
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    Problem Solving

    I have been working on this problem for about 2 hours now and can't figure out the answer. I have come up with multiple ideas but none are working.

    The question is:
    Two players play the following game: Thirteen markers are arranged in a circle. Each player removes either one marker or two contiguous markers (i.e markers that started out next to each other.) The player who takes the last marker wins. Is there a winning strategy for one of the players? If so, for which one, and what strategy? ( A winning is a rule for how to play your moves that will always lead to a win.)


    Any help would be nice. Thank you in advance!
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  2. #2
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    Quote Originally Posted by matgrl View Post
    I have been working on this problem for about 2 hours now and can't figure out the answer. I have come up with multiple ideas but none are working.

    The question is:
    Two players play the following game: Thirteen markers are arranged in a circle. Each player removes either one marker or two contiguous markers (i.e markers that started out next to each other.) The player who takes the last marker wins. Is there a winning strategy for one of the players? If so, for which one, and what strategy? ( A winning is a rule for how to play your moves that will always lead to a win.)


    Any help would be nice. Thank you in advance!
    1. I'm not sure that I understand correctly the marked text (in blue)

    2. In general: Make sure that there is a multiple of 3 left and your contrahent has to make her/his next move.
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  3. #3
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    The marked text in blue is saying that a player can either take one marker or two markers that are next to each other at a time. They can choose either one to do. Does this make sense?
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  4. #4
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    Quote Originally Posted by matgrl View Post
    The marked text in blue is saying that a player can either take one marker or two markers that are next to each other at a time. They can choose either one to do. Does this make sense?
    suppose the markers are arranged in the following order:

    abcdefghijklma...

    If a player removes e, will the other player be allowed to remove d and f in the next move ?
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  5. #5
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    This looks like a variant of Nim.
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  6. #6
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    No the player would only be able to be de, or dc since they are right next to each other.
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