Math CentralQuandaries & Queries


Question from Jim:

I have a golf trip scheduled with a total of 12 guys. We are playing three rounds of golf. For round 1 Players A B C D must play together. Is there a formula that would allow me to set up the other 8 foursomes with no repeats or minimal repeats?



On day 2 there will be at least 3 pairs who have played together before. This is because at least two members of each foursome must have been in the same foursome on day 1. The same reasoning applies to day 3. So, the best one can hope for is a schedule with 6 repeats. I don't know if one exists.

The first two rounds are easy to make. ABCD; EFGH; IJKL then ABEI; CFGK; DHKL. See what you can do for the third. If you can get a total of 8 or fewer repeats, you're doing well.

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