20 team tournament

[rdunnivan]

I have 8 juniors teams and 12 adult teams for a volleyball tournament.  Each group will be divided into pools of 4 (2 for juniors and 3 for adults).  We only have 4 courts to run this on.  I am planning to run the first 2 rounds with adults on 3 courts and juniors on 1 court so they end around the same time.  After the first two rounds, each age bracket would occupy 2 courts.  This would take 7 rounds for the juniors and 8 rounds for the adults.  Is there a best schedule where teams don't sit too many games out in a row?

[Ian Wakeling]

If the pools are called J1,J2,A1,A2 & A3, then I would start by constructing a plan that shows which court is assigned to which pool over the 8 rounds of play.

J1 A1 A2 A3
J2 A1 A2 A3
J1 J2 A1 A2
J1 J2 A3 A1
J1 J2 A2 A3
J1 J2 A1 A2
J1 J2 A3 A1
-- -- A2 A3

Then call the 4 teams in one pool A,B,C & D, and take the relevant 6 slots from the plan above in time order, and assign them to games as follows:

AB
CD
AC
BD
AD
BC

For example teams A & B in pool J1 play in round 1, while teams C & D in pool J1 play in round 3.

I can't say that this is optimal, but I think it will be close.  Each junior team will have one game in rounds 1-3, one game in rounds 4-5, and one game in rounds 6-7.  While each adult team will have one game in rounds 1-2, one game in rounds 3-5, and one game in rounds 6-8.

Hope that helps.

[rdunnivan]

I actually found this to satisfy much better.  Having the first round be all adults and then splitting into juniors and adults on 2 courts each.  No team ever sits out more than 2 games.

A1 A1 A2 A2
J1 J2 A3 A3
J1 J2 A1 A1
J1 J2 A2 A2
J1 J2 A3 A3
J1 J2 A1 A1
J1 J2 A2 A2
-- -- A3 A3