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Math Help - Combinatronics, fair matching

  1. #1
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    Combinatronics, fair matching

    I am new here, I don't know if this is the right place for this post, but...feel free to delete or move this post as necessary.

    Here is the problem:

    n players
    k players per team
    Each player must play “with” and “against” every other player at least
    once and an equal number of times using a minimal number of matches.
    An easy example:

    Players = 1, 2, 3, 4 (n = 4)
    2 players per team (k = 2)
    Matches:
    1, 2 vs. 3, 4
    1, 3 vs. 2, 4
    1, 4 vs. 2, 3
    After those 3 matches, all players played “with” and “against” each
    other once.
    As simple as it gets.

    The challenge that is causing me trouble:
    Find an efficient method to generate the minimal number of matches for
    any n and k.
    It sounded trivial at first…at first.

    Obviously, I meant:

    "After those 3 matches, all players played “with” each other once and “against” each
    other twice.
    Last edited by mr fantastic; March 12th 2011 at 04:47 PM. Reason: Merged posts.
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  2. #2
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    Thanks for moving this thread to a more suitable location.
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