Triangular Scheduling

[minnygopher]

Volleyball Scheduling.  15 teams, 7 dates, each date has 5 triangulars scheduled.  On each date, each team is grouped in triangular meets.  For example:  Teams 1, 2, 3 are grouped together.  1 vs 2, then 1 vs 3 and 2 vs 3 to finish triangular meet.  Each team will play each of the 14 teams once, 2 matches each date.

Week 1 could look like this:  1-2-3,  4-6-8, 5-7-9, 10-12-14, 11-13-15.

Should fit perfectly?  I tried, don't know if it is mathmatically possible.  So for team 1 it's easy:  Wk 1:  1-2-3.  Wk 2:  1-4-5.  Wk 3: 1-6-7.  Wk 4: 1-8-9.  Wk 5: 1-10-11.  Wk 6: 1-12-13.  Wk 7: 1-14-15.  So if you take teams 2 & 3 for Wk 2 through 7, they would be placed in different triangulars for those weeks.

If there is someone with a solution, it would be very welcomed.

Thanks!

[Ian Wakeling]

I think, if I understand you correctly, that the schedule here for 15 teams is what you are looking for.

Ian.

[minnygopher]

Ian,

Correct.  Each team must be grouped in a triangular for the 7 weeks with two different teams each week.  I like the comparison to the golf grouping of threesomes.  Hope this makes sense.  What is the formula used to come up with this?

Gerry (minnygopher)

[Ian Wakeling]

This web page might give you some idea of how the 15 player solution can be constructed.  There is a mathematical proof of the general problem, when the number of players is 3 more than a multiple of 6, however the proof can't be represented as a single formula, more likely it would translate into a computer program of several thousand lines.