Golf Problem
Subject: GOLF TRIP
Date: Wed, 19 Aug 1998 15:55:25 -0400

Twelve golfers plan to play seven rounds of golf. Each would like to play as many rounds with different golfers as possible. What are the optimum combinations to accomplish that goal?

Thanks.
Bob [old golfer]

Hi Bob

Your problem doesn't have a really nice solution when you have just 12 players and 7 matches (weeks) — it can in fact be shown that there is no ‘nice’ solution.
The following chart gives a method for an 8 game schedule (from which you could take seven of the weeks). In the schedule every pair appears together either 2 or 3 times and it avoids any triple being repeated.

First
foursome
Second
foursome
Third
foursome
week
1
1  2  3  4  5  6  7  8  9  10 11 12
week
2
1  2  8  11 3  5  6  12 4  7  9 10
week
3
1  4  6  10 2  5  9  11 3  7  8  12
week
4
2  5  8  10 1  3  6  9  4  7  11 12
week
5
2  6  9  12 1  5  7  10 3  4  8  11
week
6
1  7  8  9  2  4  5  12 3  6  10 11
week
7
1  5  11 12 4  6  8  9  2  3  7  10
week
8
3  4  5  9  1  8  10 12 2  6  7  11
Cheers,
Denis

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