Math CentralQuandaries & Queries


Question from evan:

I have a group of 6 golfers playing 8 rounds. we would like to rotate the 3 somes so each person golfs with different people as many times as possible


There are exactly 20 ways to choose groups of three from your 6 golfers, which means that in TEN rounds, all possible pairs of threesomes would be used exactly once, so that each pair of golfers would play together in exactly four rounds. The best you can do in only 8 rounds is to drop two of the ten possible rounds, which necessarily will mean that some pairs will play together only twice, while others play together three or four times. Here is a systematic list of the twenty threesomes. For your eight rounds together, just delete any two rows of the table; for example, if you delete the final two rows, the pairs 1&6 and 2&3 will play together only twice.

round 1 123 456
round 2 124 356
round 3 125 346
round 4 126 345
round 5 134 256
round 6 135 246
round 7 136 245
round 8 145 236
round 9 146 235
round 10 156 234


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