Triple Round Robin 11 players with a twist.

[oman_2]

I have 11 players participating in a tournament where each player will play each other player 3 times. The twist is that 4 players play together at once.

So players A, B, C, and D all play in the first match.
So that counts as
A playing B
A playing C
A playing D
B playing C
B playing D
C playing D

I started myself by putting the letter together fairly randomly and keeping track of who has played who but found myself lost.
Some players ended up short matches against people and others had to many. I couldn't even figure out how many matches there are suppose to be.

Please Help me!!

[Ian Wakeling]

It will not be possible to find a perfect solution.

With 11 players there are 11*10/2 or 55 possible pairings.  You wish them to play 3 times, so a total of 165 pairings, but unfortunately a number that is not divisible by 6, the number of pairings per round.

Cyclic schedules for multiples of 11 rounds may be suitable as this has the advantage of giving every player the same number of matches.  For example this plan

   1   :   5   6  10   1
   2   :   6   7  11   2
   3   :   7   8   1   3
   4   :   8   9   2   4
   5   :   9  10   3   5
   6   :  10  11   4   6
   7   :  11   1   5   7
   8   :   1   2   6   8
   9   :   2   3   7   9
  10   :   3   4   8  10
  11   :   4   5   9  11
  12   :   5   2  10  11
  13   :   6   3  11   1
  14   :   7   4   1   2
  15   :   8   5   2   3
  16   :   9   6   3   4
  17   :  10   7   4   5
  18   :  11   8   5   6
  19   :   1   9   6   7
  20   :   2  10   7   8
  21   :   3  11   8   9
  22   :   4   1   9  10
  23   :   5   2   6   3
  24   :   6   3   7   4
  25   :   7   4   8   5
  26   :   8   5   9   6
  27   :   9   6  10   7
  28   :  10   7  11   8
  29   :  11   8   1   9
  30   :   1   9   2  10
  31   :   2  10   3  11
  32   :   3  11   4   1
  33   :   4   1   5   2

gives 22 of the 55 pairs exactly 3 matches, while the remaining 33 pairs get 4 matches.

While this plan:

   1   :  11   1   2   8
   2   :   1   2   3   9
   3   :   2   3   4  10
   4   :   3   4   5  11
   5   :   4   5   6   1
   6   :   5   6   7   2
   7   :   6   7   8   3
   8   :   7   8   9   4
   9   :   8   9  10   5
  10   :   9  10  11   6
  11   :  10  11   1   7
  12   :   7   3   9   1
  13   :   8   4  10   2
  14   :   9   5  11   3
  15   :  10   6   1   4
  16   :  11   7   2   5
  17   :   1   8   3   6
  18   :   2   9   4   7
  19   :   3  10   5   8
  20   :   4  11   6   9
  21   :   5   1   7  10
  22   :   6   2   8  11

gives 33 of the pairs exactly 2 matches, while the remaining 22 pairs get 3 matches.

Hope that helps.