Three concurrent knockout tournaments
Posted: Mon Nov 29, 2010 1:57 pm
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)
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)