Math CentralQuandaries & Queries


Question from Erich:

i have to make a sports schedule for the ymca. i have 7 teams. they need to play each other 2 times. we have 3 time slots per night. i would like them to have an even number of time slots thru the season. one team must have abye each week. can you chow mw the schedul. example time 1 team 1 vs. team 2. time 2 team 3 vs. team 4 time 3 team 5 vs. team 6. team 7 bye week 1.


Try this:

1: 2-7; 3-6; 4-5
2: 1-3; 4-7; 5-6
3: 2-4; 1-5; 6-7
4: 3-5; 2-6; 1-7
5: 4-6; 3-7; 1-2
6: 5-7; 1-4; 2-3
7: 1-6; 2-5; 3-4

If you assign the times from left to right on each day, then each team plays twice at each time during the first 7 weeks. For the second seven weeks you could repeat the first 7 changing home and away, and maybe changing the time slots so that the games go in slots 2, 3, 1 from left to right in each row. To be a bit more fancy, change the numbers by replacing all 1's by 4's, all 2's by 5's, all 3's by 6's, all 4's by 7's, all 5's by 1's, all 6's by 2's and all 7's by 3's. Any collection of replacements where all 7 numbers still appear will work. The time slots will still work out as before.

Hope this makes sense.

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