Question 967817: I want to put a tennis schedule together. There will be 12 players or six double teams. I need a schedule that in 11 matches no one plays anyone twice.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you have 6 double teams.
out of those 6 double teams, you can make c(6,2) combinations where each pair is different.
c(6,2) is equal to 6! / (2! * 4!) which is equal to (6*5)/2 = 15 different combinations where order is not important.
order is not important means that ab and ba count as one game, not two.
if order was important, they would count as two games.
let the teams be labeled team a, b, c, d, e, f.
the 15 possible different combinations where order is not important are:
ab
ac
ad
ae
af
bc
bd
be
bf
cd
ce
cf
de
df
ef
if you want every team to play every other team where no teams plays the same team twice, then you can schedule 15 matches and that will do it.
otherwise, if you can only schedule 11 matches, then pick any 11 out of the 15.
you might want to count how many games each team is in so you can even it up as much as possible.
for example:
ab counts as one for a and one for b.
bc counts as one for b and one for c.
total for a is 1
total for b is 2
total for c is 1.
cd counts as one for c and one for d.
total for c is now 2.
total for d is 1.
etc.
the goal is to even up the number of games as much as possible.
you won't be able to make each team play exactly the same number of games, but you can make them more or less even.
one possible arrangement would be:
ab
ac
af
bc
bd
be
cd
ce
de
df
ef
you have a count of:
a = 3
b = 4
c = 4
d = 4
e = 4
f = 3
add them up and they total 22.
divide that by 2 and you get 11 games.
that's about as even as you'll be able to get it with 11 games.
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