Golf Pairings - 10 Players

[tomc]

Hello,

Wonderful to have a site dedicated to complex Math Questions.

My Problem is trying to build a Matrix for an upcoming Jamaica Golf Trip.  Here's the details:

10 Players
5 Players in two groups each day; 2 - Fivesomes
6 Total rounds

Want to spread out the players (1-10) as equal as possible.
So everyone can play with each other 3-5 times each; no less than 2.

Thanks for your help.  

[Ian Wakeling]

There are no good solutions to this problem.  With 45 pairs of players among 10, the best schedule possible will have 30 of those pairs playing together twice and 15 pairs playing together 4 times.  For example:

  10   4   5   8   6
  2   3   1   7   9

  10   8   4   1   7
  5   2   9   6   3

  7   6   1   9   4
  5   8  10   2   3

  2  10   4   7   3
  1   5   6   9   8

  4  10   9   2   6
  5   7   3   8   1

  8   2   9   1  10
  6   3   4   7   5

[tomc]

Ian

Thanks for the quick response. I appreciate your help.  8-)

Tomc