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Math Help - Difficult Math Scheduling Problem

  1. #1
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    Difficult Math Scheduling Problem

    The goal is to make a schedule that will allow 8 teams to play each of 4 games once without playing the same team twice.

    For instance,
    Games 1 Game 2 Game 3 Game 4
    Week 1 1 vs 8 2 vs 7 3 vs 6 4 vs 5
    Week 2
    Week 3
    Week 4

    In week 2, each team must play a different game without ever playing a team that they have previously face.
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  2. #2
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    Re: Difficult Math Scheduling Problem

    1-2, 3-4, 5-6, 7-8
    1-3, 2-4, 5-7, 6-8
    1-4, 2-3, 5-8, 6-7
    1-5, 2-6, 3-7, 4-8
    Check:
    1: 2,3,4,5
    2: 1,3,4,6
    3: 1,2,4,7
    4: 1,2,3,8
    5: 1,6,7,8
    6: 2,5,7,8
    7: 3,5,6,8
    8: 4,5,6,7
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  3. #3
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    Re: Difficult Math Scheduling Problem

    Quote Originally Posted by Wilmer View Post
    1-2, 3-4, 5-6, 7-8
    1-3, 2-4, 5-7, 6-8
    1-4, 2-3, 5-8, 6-7
    1-5, 2-6, 3-7, 4-8
    Check:
    1: 2,3,4,5
    2: 1,3,4,6
    3: 1,2,4,7
    4: 1,2,3,8
    5: 1,6,7,8
    6: 2,5,7,8
    7: 3,5,6,8
    8: 4,5,6,7
    I do not understand your answer. Is it in the same format as my table? If so, teams are playing the same game twice
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  4. #4
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    Re: Difficult Math Scheduling Problem

    Quote Originally Posted by ben61693 View Post
    The goal is to make a schedule that will allow 8 teams to play each of 4 games once without playing the same team twice.
    Well then, what does this mean: "play each of 4 games once"?

    EDIT:
    ok ok ! Think I see what you mean:
    in your example, team1 cannot play team8 again, PLUS both teams cannot appear under Game1 again; yes?

    Tried a bit: can only come close

    I'll keep trying...YOU try too
    Last edited by Wilmer; May 11th 2012 at 07:32 AM.
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  5. #5
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    Re: Difficult Math Scheduling Problem

    Here you go:
    Code:
         G1   G2   G3   G4
    W1   12   34   56   78
    W2   35   17   28   46
    W3   48   26   37   15
    W4   67   58   14   23
    No charge
    Thanks from ben61693
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  6. #6
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    Re: Difficult Math Scheduling Problem

    Quote Originally Posted by ben61693 View Post
    The goal is to make a schedule that will allow 8 teams to play each of 4 games once without playing the same team twice.

    For instance,
    Games 1 Game 2 Game 3 Game 4
    Week 1 1 vs 8 2 vs 7 3 vs 6 4 vs 5
    Week 2
    Week 3
    Week 4

    In week 2, each team must play a different game without ever playing a team that they have previously face.
    Quote Originally Posted by Wilmer View Post
    Here you go:
    Code:
         G1   G2   G3   G4
    W1   12   34   56   78
    W2   35   17   28   46
    W3   48   26   37   15
    W4   67   58   14   23
    No charge
    Thank you so much. I kept getting 3vs5 twice for some reason. Just out of curiosity. How did you do it? Pure guessing or some strategy involved?
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  7. #7
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    Re: Difficult Math Scheduling Problem

    Wrote short computer program to do about half a case; trial and error for other half.
    Here's another solution:
    Code:
         G1   G2   G3   G4
    W1   17   45   28   36
    W2   26   38   15   47
    W3   35   27   46   18
    W4   48   16   37   25
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  8. #8
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    Re: Difficult Math Scheduling Problem

    By the way, your problem really is:
    You have 28 2digit numbers:
    12,13,14,15,16,17,18,23,24,25,26,27,28,34,35,36,37 ,38,45,46,47,48,56,57,58,67,68,78
    Enter 16 of these numbers in a 4 by 4 array such that:
    1: the 4 numbers in each row are made up of all digits 1 to 8
    2: the 4 numbers in each column are made up of all digits 1 to 8

    This makes it relatively easy to write a computer program.
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