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| Math Central | Quandaries & Queries |
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Question from Tom: We would like to play a ryder cup format with two teams of 4 playing 4 rounds of golf. Three of the rounds would be pairs playing each other and one round would be singles. How can we set up the foursomes so we balance the number of times we play with every other golfer. |
Tom,
I am not certain I know exactly what you mean, but here goes. Let's call the teams A and B, and the players a1, a2, a3, a4, and b1, b2, b3, b4, respectively.
You're looking at the four sets of pairings that have each player with A with each player from B.
- a1b1, a2b2, a3b3, a4b4
- a1b2, a2b3, a3b4, a4b1
- a1b3, a2b4, a3b1, a4b2
- a1b4, a2b1, a3b2, a4b3
It isn't possible to perfectly balance the foursomes. You can perfectly balance the A's against the B's by always putting a1 and a2 out in the same foursome (any two A's would work). Otherwise, in an ideal world some pairs would be together twice and others only once. Unfortunately the world isn't ideal and the arrangement that's hoped for does not exist. We have checked by computer that, with 8 players, any collection of foursomes will have some pairs together three times.
--Victoria
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