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| Math Central | Quandaries & Queries |
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Question from George: I have 12 golfers and want to set up a season schedule that will avoid duplication of playing partners as much as possible. The season is 24 weeks long. Do you have a formula? |
George,
I can't promise that the schedule below is best possible as the number of schedules is too big to verify that by computer. It is really really good according to the assessment scheme we use to determine "best" though. I hope it with suit your purposes.
On each day below, the players correspond to the 12 positions in the list and the numbers indicate the foursomes. On day 0 (the first day), the groups are 1, 2, 3, 4; 5, 6, 7, 8; 9, 10, 11, 12, and on day 1 they are 1, 2, 5, 9; 3, 6, 7, 10; 4, 8, 11, 12.
The order of the days and the numbering of the groups on each day can be changed without affecting anything. Maybe put the 24 days in a hat and draw them out to make your schedule? Then, for each day put the three foursomes in a hat and draw randomly to get the tee-off order?
Day 0 : (0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2)
Day 1 : (0, 0, 1, 2, 0, 1, 1, 2, 0, 1, 2, 2)
Day 2 : (0, 1, 0, 2, 0, 1, 2, 1, 2, 1, 0, 2)
Day 3 : (0, 1, 1, 2, 1, 2, 0, 0, 2, 0, 2, 1)
Day 4 : (0, 0, 1, 2, 2, 0, 1, 1, 1, 2, 2, 0)
Day 5 : (0, 1, 0, 0, 2, 0, 2, 1, 1, 2, 1, 2)
Day 6 : (0, 1, 1, 0, 2, 2, 1, 0, 2, 0, 1, 2)
Day 7 : (0, 1, 2, 1, 1, 2, 0, 1, 2, 2, 0, 0)
Day 8 : (0, 1, 2, 2, 0, 1, 1, 0, 0, 2, 1, 2)
Day 9 : (0, 1, 2, 1, 0, 2, 1, 2, 1, 0, 0, 2)
Day 10 : (0, 0, 1, 2, 2, 2, 2, 1, 0, 0, 1, 1)
Day 11 : (0, 1, 2, 0, 2, 0, 1, 2, 2, 1, 0, 1)
Day 12 : (0, 1, 0, 1, 1, 2, 0, 2, 0, 2, 2, 1)
Day 13 : (0, 1, 1, 1, 2, 0, 2, 0, 2, 1, 2, 0)
Day 14 : (0, 1, 1, 0, 1, 2, 0, 0, 2, 2, 1, 2)
Day 15 : (0, 0, 1, 1, 2, 0, 2, 2, 1, 2, 0, 1)
Day 16 : (0, 0, 1, 2, 1, 1, 0, 2, 2, 1, 2, 0)
Day 17 : (0, 1, 0, 2, 2, 2, 2, 1, 1, 1, 0, 0)
Day 18 : (0, 1, 1, 2, 0, 1, 2, 1, 0, 2, 2, 0)
Day 19 : (0, 1, 0, 0, 1, 2, 2, 1, 2, 0, 2, 1)
Day 20 : (0, 1, 0, 1, 2, 1, 0, 0, 1, 2, 2, 2)
Day 21 : (0, 1, 1, 2, 0, 2, 1, 2, 0, 0, 1, 2)
Day 22 : (0, 0, 1, 2, 2, 0, 1, 2, 1, 0, 2, 1)
Day 23 : (0, 1, 2, 1, 0, 0, 0, 2, 2, 1, 2, 1)
Have some fun!
--Victoria
In May 2017 Colin wrote in response to this posting.
If there are 4 0's, 1's & 2's, how do you determine which 0,1 or 2 moves where for the following game. Could you show it as player A,B,C,D, E,F,G,H, I,J,K,L, that way I could follow which group they would be in for each game
Thanking you in advance
Colin
Colin,
I am going to add a row to the table to indicate the golfers. As you suggested I am naming the A, B, C, D, E, F, G , H, I, J, K am\nd L.
| Golfers | A |
B |
C |
D |
E |
F |
G |
H |
I |
J |
K |
L |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Day 0 | 0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
2 |
2 |
2 |
2 |
| Day 1 | 0 |
0 |
1 |
2 |
0 |
1 |
1 |
2 |
0 |
1 |
2 |
2 |
| Day 2 | 0 |
1 |
0 |
2 |
0 |
1 |
2 |
1 |
2 |
1 |
0 |
2 |
| Day 3 | 0 |
1 |
1 |
2 |
1 |
2 |
0 |
0 |
2 |
0 |
2 |
1 |
| Day 4 | 0 |
0 |
1 |
2 |
2 |
0 |
1 |
1 |
1 |
2 |
2 |
0 |
| Day 5 | 0 |
1 |
0 |
0 |
2 |
0 |
2 |
1 |
1 |
2 |
1 |
2 |
| Day 6 | 0 |
1 |
1 |
0 |
2 |
2 |
1 |
0 |
2 |
0 |
1 |
2 |
| Day 7 | 0 |
1 |
2 |
1 |
1 |
2 |
0 |
1 |
2 |
2 |
0 |
0 |
| Day 8 | 0 |
1 |
2 |
2 |
0 |
1 |
1 |
0 |
0 |
2 |
1 |
2 |
| Day 9 | 0 |
1 |
2 |
1 |
0 |
2 |
1 |
2 |
1 |
0 |
0 |
2 |
| Day 10 | 0 |
0 |
1 |
2 |
2 |
2 |
2 |
1 |
0 |
0 |
1 |
1 |
| Day 11 | 0 |
1 |
2 |
0 |
2 |
0 |
1 |
2 |
2 |
1 |
0 |
1 |
| Day 12 | 0 |
1 |
0 |
1 |
1 |
2 |
0 |
2 |
0 |
2 |
2 |
1 |
| Day 13 | 0 |
1 |
1 |
1 |
2 |
0 |
2 |
0 |
2 |
1 |
2 |
0 |
| Day 14 | 0 |
1 |
1 |
0 |
1 |
2 |
0 |
0 |
2 |
2 |
1 |
2 |
| Day 15 | 0 |
0 |
1 |
1 |
2 |
0 |
2 |
2 |
1 |
2 |
0 |
1 |
| Day 16 | 0 |
0 |
1 |
2 |
1 |
1 |
0 |
2 |
2 |
1 |
2 |
0 |
| Day 17 | 0 |
1 |
0 |
2 |
2 |
2 |
2 |
1 |
1 |
1 |
0 |
0 |
| Day 18 | 0 |
1 |
1 |
2 |
0 |
1 |
2 |
1 |
0 |
2 |
2 |
0 |
| Day 19 | 0 |
1 |
0 |
0 |
1 |
2 |
2 |
1 |
2 |
0 |
2 |
1 |
| Day 20 | 0 |
1 |
0 |
1 |
2 |
1 |
0 |
0 |
1 |
2 |
2 |
2 |
| Day 21 | 0 |
1 |
1 |
2 |
0 |
2 |
1 |
2 |
0 |
0 |
1 |
2 |
| Day 22 | 0 |
0 |
1 |
2 |
2 |
0 |
1 |
2 |
1 |
0 |
2 |
1 |
| Day 23 | 0 |
1 |
2 |
1 |
0 |
0 |
0 |
2 |
2 |
1 |
2 |
1 |
Each day the golfers are divided into two foursomes called 0, 1 and 2. Each player determines which foursome he or she belongs to by reading down his or her column. Notice that golfer A is always in foursome 0. Look now, for example at golfer H. His column starts 1, 2, 1, 0, 1. Thus on Day 0 he is in foursome 1, on Day 1 he is in foursome 2, on Days 2 he is in foursome 1, on Day 3 he is in foursome 0 and on Day 4 he is in foursome 1.
If you read across each row you can see the foursomes on that day. For example on Day 14 the foursomes are
0: A, D, G, H
1: B, C, E, K
2: F, I, J, L
I hope this explains Victoria's table. Write back if you need more assistance.
Penny
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