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 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

Evan,

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.

 FIRST GROUP SECOND GROUP 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

Chris

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