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| Math Central | Quandaries & Queries |
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A golf Pairing question: 8 Golfers are Playing golf - one round per day Four days of golf (four twosomes) are paired each day to play ***No one can play with the same partner more than once ***Everyone must play with every other golfer in his foursome at least once Is this possible? |
Yes. In fact the second requirement can be achieved in 3 days:
AB,CD EF,GH (1)
AE,BF CG,DH (2)
AG,BH EC,FD (3)
On the fourth day there are various possibilities:
AD,EH BC,FG (4)
AC,EG BD,FH (4')
AF,CH BE,DG (4")
AH,CF BG,DE (4'")
Indeed, you can use (1-3) and as many of the 4's as needed to go anywhere from 3 to 7 days under these rules. You can also redivide the pairs of each of the "4" pairings into foursomes in two other ways, giving a lot of choices.
-RD
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