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| Math Central | Quandaries & Queries |
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Question from John, a parent: 8 of us are going on a golf trip next month. We are golfing 5 rounds. Is there any way that everyone can play with each other at least twice? I checked the archives but did not notice this particular question. Thanks for your help. |
A symmetric arrangement would be easy with 7 rounds: the numbers would then work out perfectly for each golfer to play three rounds with each other golfer. With only 5 rounds it might at first seem possible for every pair to play together twice, with just one pair together three times. However the best I can do with five rounds is to have each participant play with one person in only one round, with two people in three rounds, and with the remaining four in two rounds. The accompanying schedule is for seven rounds, so you will just play five of them. If you choose the first five, for example, then players 1 and 7 will be together just once, as will 2 and 4, 3 and 6, and 5 and 8.
| First Group | Second Group | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| day 1 | 8 | 4 | 6 | 7 | 1 | 2 | 3 | 5 | ||
| day 2 | 8 | 5 | 7 | 1 | 2 | 3 | 4 | 6 | ||
| day 3 | 8 | 6 | 1 | 2 | 3 | 4 | 5 | 7 | ||
| day 4 | 8 | 7 | 2 | 3 | 4 | 5 | 6 | 1 | ||
| day 5 | 8 | 1 | 3 | 4 | 5 | 6 | 7 | 2 | ||
| day 6 | 8 | 2 | 4 | 5 | 6 | 7 | 1 | 3 | ||
| day 7 | 8 | 3 | 5 | 6 | 7 | 1 | 2 | 4 | ||
Chris
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