Three concurrent knockout tournaments

[Jon Corby]

I'm helping to organise a 'fun' event for my department this Friday, which involves us splitting into eight teams and competing at three different games in three separate knockout tournaments. These tournaments will all be running alongside each other, so I need to work out a schedule that will try, as far as is possible, to avoid

a) teams being required to play different games at the same time
b) teams meeting the same teams in each of the three tournaments.

I'm probably going to write a quick program tonight to run through all permutations and come up with some kind of "best" plan, but just in case that's unnecessary can any of the more mathematically-minded steer me in the right direction?

Assume that Game 1's schedule is:

QF1 - A v B
QF2 - C v D
QF3 - E v F
QF4 - G v H

SF1 - Winner of QF1 v QF2
SF2 - Winner of QF3 v QF4

Final.

What should Game 2 & Game 3's schedule be? (Assume that the three different games take the same amount of time to play)

[James Hall]

The schedule below should be pretty good - it (just about) minimises the risk of teams meeting each other in the semis who they've played at another game in the quarters. It also makes sure the QFs can take place all simultaneously (assuming that all the games take the same amount of time). You can't cater for every QF result with regards to scheduling the semi-finals, so it's best to just wing it and try to arrange the order they're played to minimise disruption during the event.

I didn't worry so much about the finals because I figured everyone who's been knocked out by that point will want to watch them.
---
Game 1
(1) A v B
(2) C v D
(3) E v F
(4) G v H
-
(A/B) v (C/D)
(E/F) v (G/H)
-
(A/B/C/D) v (E/F/G/H)
---
Game 2
(1) E v G
(2) F v H
(3) B v D
(4) A v C
-
(B/D) v (F/H)
(A/c) v (E/G)
-
(A/C/E/G) V (B/D/F/H)
---
Game 3
(1) C v F
(2) B v G
(3) A v H
(4) D v E
-
(A/H) v (B/G)
(D/E) v (C/F)
-
(A/B/G/H) v (C/D/E/F)

[Jon Corby]

Cheers James - you're right that it's not worth worrying about the quarter finals too much as it should be easy to arrange them to avoid clashes, and if it isn't possible then tough. I've just set off a "brute force" program to try and minimise the clashes both in timing and potential fixtures, I reckon it should come out similar to yours above. Ah, actually, maybe not - typically (i.e. stupidly), I'd completely overlooked the fact that the semi finals didn't have to be QF1 v QF2 time-wise, so I've probably ended up restricting my program a bit too much. Or it might not make any difference, I'm not sure. I get confused trying to think about these things like this, I always end up counting on my figures and double-checking the simplest of calculations on paper.