Math CentralQuandaries & Queries


Question from Gregg:

We have 6 golfers playing in threesomes for three rounds of golf. I would like each golfer to play equally with the other 5. How can this be done.


I wrote a program that looks at all of the possible schedules and comes up with one that's "most balanced". Here it is what it found. The positions are the players and the numbers are the group they are in.

Day 1 : (0, 0, 1, 0, 1, 1)
Day 2 : (0, 1, 0, 1, 0, 1)
Day 3 : (0, 0, 0, 1, 1, 1)

You'll notce that, for example, players 1 and 6 never play together. There isn't a schedule where every pair of players plays together at least once, otherwise the program would have found it. It looks like the best that can be done is that some pairs are together twice, and some not at all. That's too bad. It seems the arrangement you want just isn't possible.


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS