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Math Help - can 17 teams play 14 games each ?

  1. #1
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    can 17 teams play 14 games each ?

    My neighbor runs a basketball league and asked me (a computer programmer) to generate a list of match ups for him. I readily accepted, but it's turning out harder than I thought.

    Is it really possible to have 17 teams each play 14 games such that they don't play each other twice?

    I am beginning to suspect that it's not possible - for instance, I've proven by trial and error that you can't get 5 teams to play 3 games.

    Is there a general formula I can use to determine whether a given number of teams can play a given number of games w/o playing each other twice?
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  2. #2
    Junior Member
    Joined
    Jan 2009
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    How about brute force to help us in this problem?

    Pick one team from 17 teams, and then decide arbitrarilty their 14 oppnenets, let's mark the teams as 1-17.
    then: 1 will face 2-15.
    2 will face 1 and 3-15.
    3 will face 1 and 2 and 4-15.
    4 will face 1 and 2 and 3 and 5-15.
    5 will face 1,2,3,4 and 6-15.
    6 will face 1,2,3,4,5 and 7-15
    7 will face 1,2,3,4,5,6 and 8-15.
    8 will face 1,2,3,4,5,6,7 and 9-15.
    9 will face 1-8 and 10-15.
    10 will face 1-9 and 11-15
    11 will face 1-10 and 12-15
    12 will face 1-11 and 13-15
    13 will face 1-12 and 14-15
    14 will face 1-13 and 15.
    15 will face 1-14.
    Now for 16 and 17 you have the freedom to choose which they should play against, because we have 15 teams to choose from.

    I might have some errors as I haven't checked it thoroughly.
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