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| Math Central | Quandaries & Queries |
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Question from Kelly, a parent: Hi there. Some of your posts are close&, but my problem is evening out the home and away games. We have 6 teams in our league and we are going to play a 20 game schedule, playing everyone 4 times. We will play Fridays and Saturdays, each weekend. Of course the ideal would be to have each team have a home and an away game each weekend, but I realize that is impossible, but I would like it as close as possible. Any help would be much appreciated!! We also were considering opening with a home and away - Friday then Saturday with the same teams. Then carrying on with playing everyone else and then possibly finishing up with the same home and home. |
Kelly,
There is not a perfect solution. You'll need to choose an option that works with your league’s circumstances.
For six teams playing each other once, there is a schedule with (only) four instances of teams playing home twice in a row or away twice in a row. This is the best possible. If you use this schedule, then use it again with home and away reversed, then again as the first time through, then again as the second time through, that’s not too bad.
There are schedules with fewer interruptions in the pattern, but the games are not equally spread through the season. One example would be if the same two teams played each other home and away for the first 4 games, and then moved on to two other opponents.
Another one would be where a team played the same opponent home and away on Friday and Saturday, and you went through the schedule twice. I
Here is a schedule that is like the one discussed in the first couple of sentences. Home teams are listed last.
16, 25, 34
62, 31, 45
63, 24, 51
46, 35, 12
56, 14, 23
Good luck.
—Victoria
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