Math CentralQuandaries & Queries


Question from Chris, a parent:

8 golfers playing 2 groups of 4 each day for 5 days.
Trying to work out how they can organise playing at least once, and no more than twice, with everyone over the 5 days.
We always come up with someone playing 3 times with another in one of the 4's!
Hope you can help!


It isn't possible. If every pair played together two times, there would be 56 "play together" pairs. Every foursome accounts for six such pairs, That's 12 per day, so over 5 days there are 60 pairs. That means some people must play together three times. The theoretical minimum number of pairs that would play together three times is four. I don't know if that can be achieved.

Maybe the schedule you have is ok?

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