Math CentralQuandaries & Queries


Question from Toni:

I need to create a doubles tennis schedule for 6 players playing over a 32 week schedule where no player repeats with a partner.


There are only 15 possible pairs of partners, so this isn't possible. At the very least there will be some pairs who are partnered three times. If you can phrase your question to take that into account, then maybe I can suggest how the schedule can be made.

Good luck!

Toni replied

I need a doubles tennis schedule for 6 players over a 32 week schedule
where we play one time per week


There are 15 ways of pairing up 6 players. They come in 5 groups of 3 pairs. For example 12, 34, 56 is one of the collections of 3 pairs. Another group is 12, 35, 46.

For each collection of 3 pairs, there are 3 weeks worth of matches. For the collection 12, 34, 56 above: 12 v 34; 12 v 56; 56 v 34. In total that is 15 weeks worth of matches.

What I suggest is to write down the 15 weeks worth of matches, and then shuffle them around so people don't have the same partner on consecutive weeks. Hopefully it is possible to do this so that no person misses 2 consecutive weeks, unless that is desirable. I'd then take the same 15 you started with and shuffle them around differently, or maybe even just repeat them, to get the next 15 weeks. The last 2 weeks can be filled in any way you want.

Good luck!

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