10 Team Quiz League with 3 Triangular Meets Per Night

[HillJackBob]

Hello.  I'm a coach in an elementary school quiz league where our conference includes 10 teams.  Each night we have 3 triangular meets at 3 locations, and each week 1 team has the night off.  Right now the schedule is all messed up, there are 9 dates, some teams are playing each other 3 times, some just once, some teams have 0 byes, some have 1 bye week, and some have 2.  It's chaos.

I'd like to try to see if I could come up with a schedule with a 10th date, so therefore every team could have one bye week.  In that scenario, everyone SHOULD be able to play each other twice.  Can anyone direct me to a way to arrange these teams in this way.

i.e.  the first week could be (A B C) (D E F) (G H I) with team J on bye.  After 10 weeks, each team should have 1 bye, and have played each of the other teams twice.

[Ian Wakeling]

No need for chaos, there is schedule for this scenario.  For example take the 3 triangles from each of the 10 rows below and that is your 10 round schedule.



Notice that the 10 columns numbered 1 to 10 may also prove useful.  Each column could be a quiz master provided by one of the schools, so for example school 1 provides the quiz master in column 1 and they ask the questions for the 3 triangles in rounds 2, 6 & 9, if you do this for all the columns then no quiz master will ever ask the questions for a triangle that includes their own school.  The columns could also be the school who hosts, so no team competes at their own school.

I think I have it arranged so that the two occasions when a particular pair of teams meet are never in consecutive rounds.  Hope that helps.

[HillJackBob]

You are a godsend!   Thank you so much!

I've been in touch with the conference about making some needed changes, and hopefully, passing this along to them will allow them to see it my way.