 |
| ||
| |||
|
| Math Central | Quandaries & Queries |
|
Question from Evan: We are going on a golf trip to Scotland and are trying to work out the pairings. There are 8 of us playing 7 rounds. We would like to be partnered up in 2's with everyone once and have evenly split up foursomes. Thanks for the help |
Evan,
It turns out that there is a schedule whereby every 2 players are in the same foursome exactly three times. It is pasted below. The 8 players are the positions in the sequence, and the numbers indicate the two foursomes (numbered 0 and 1 for convenience only). For example, on Day 0 the foursomes are 1, 2, 3, 4; 5, 6, 7, 8; and on Day 1 they are 1, 2, 5, 6; and 3, 4, 7, 8.
Day 0 : (0, 0, 0, 0, 1, 1, 1, 1)
Day 1 : (0, 0, 1, 1, 0, 0, 1, 1)
Day 2 : (0, 1, 0, 1, 0, 1, 0, 1)
Day 3 : (0, 1, 1, 0, 1, 0, 0, 1)
Day 4 : (0, 0, 1, 1, 1, 1, 0, 0)
Day 5 : (0, 1, 0, 1, 1, 0, 1, 0)
Day 6 : (0, 1, 1, 0, 0, 1, 1, 0)
Another answer can be found here: http://mathcentral.uregina.ca/QQ/database/QQ.09.13/h/brian1.html
—Victoria
| ||
| ||
| ||
 |
 |
|
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.