Math CentralQuandaries & Queries


Question from Richard:

Hi Guys,
I have a scheduling problem which I don't think you have covered before.
Apologies if you have!
I have 17 golfers due to play 4 rounds of golf.
Each round will consist of 3 threeballs and 2 fourballs (ie. 17 golfers in 5 groups)!
Is it possible to come up with a schedule where each golfer plays
with different partners in each round?
I really hope that you can help me with this.

Hi Richard,

Here's a method that would even run to a fifth round.

Set your players up in a 4x5 grid with 3 "blanks" representing round 1

a b c *
d e f *
g h i *
j k l m
n o p q

Now slide the rows up 0,1,2,3 places.

a e i m
d h l q
g k p *
j o c *
n b f *

And do it again:

a h p *
d k c *
g o f m
j b i q
n e l *

And again:

a k f q
d o i *
g b l *
j e p *
n h c m

(And once more:

a o l *
d b p m
g e c q
j h f *
n k i * )

With a fifth round this would guarantee that everybody played the same number of threeball and fourball rounds, too.

This idea will work any time the number of groups is a prime number and no bigger than the number of players per group. So you could use it for 23 players in 3 fiveball and two fourball groups, or eight players in two threesomes and a pair. (If you didn't mind odd group sizes you could "play the columns" for a sixth round with no repetitions.)

Good Hunting!


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