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| Math Central | Quandaries & Queries |
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Duane, a parent: We have a golf outing coming up with 25 golfers playing 5 rounds in 5-somes. Is there a formula to figure out where everyone can play with different people each round? Thanks, Duane |
Duane,
It is possible, though for each person to play with every other person there would have to be 6 lines.
To find the fivesomes, start with number 1, 2, ..., 25 in a 5x5 grid:
| 1 | 2 | 3 | 4 | 5 |
| 6 | 7 | 8 | 9 | 10 |
| 11 | 12 | 13 | 14 | 15 |
| 16 | 17 | 18 | 19 | 20 |
| 21 | 22 | 23 | 24 | 25 |
Day 1: the rows
Day 2: the columns
Day 3: one from each row advancing one position each time (and wrapping around): 1, 7, 13, 19, 25; 2, 8, 14, 20, 21; etc
Day 4: one from each row advancing two positions each time (and wrapping around): 1, 8, 15, 17, 24; etc
Day 5: one from each row advancing three positions each time (and wrapping around): 1, 9, 12, 20, 23; etc
As you might expect, if there were a sixth day, you'd get the fivesomes by advancing 4 positions each time.
I hope this makes sense.
Victoria
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