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| Math Central | Quandaries & Queries |
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Question from Lorraine: I need to create a tennis schedule. We have 8 players, but only 4 play at one time. I need to create a schedule for 34 matches, but of the 34 each player plays 17 times. Each player must also play with each of the other 7 the same number of times. For instance player 1 will play 17 times, and will play with the other players the same number of times as player 2 does. Is this even possible? |
Lorraine,
- We have 8 players, but only 4 play at one time.
- I need to create a schedule for 34 matches,
- but of the 34 each player plays 17 times.
- Each player must also play with each of the other 7 the same number of times.
- For instance player 1 will play 17 times, and will play with the other players the same number of times as player 2 does.
I don't think (E) is what you mean: every time player 1 plays, he or she plays with the other players - solo tennis is a bore!
If you mean by (A-D) that player 1 plays with player 2 as often as with player 3 (etc), then that is not possible. Over 17 games, the total number of spots on court with 1 is 3x17 = 51, and this is not divisible by 7. So those 51 spots cannot be divided equally among the 7 other players.
-RD
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