Question

5 teams are participating in a tournment; each team will play every other team; win = 1 point; lose = 0 point

Answer 1

How many total permutations are possible in points table

Answer 2

for example, below is one possible permutation :
4 3 2 1 0

it means :
first team : win = 4, lose = 0
second team : win = 3, lose = 1
third team : win = 2, lose = 2
fourth team : win = 1, lose = 3
fifth team : win = 0, lose = 4

Answer 3

help !

Answer 4

do you have an answer?

Answer 5

2^5?

Answer 6

You use combinations for this.

Answer 7

yes

Answer 8

I have been trying from last couple of days

Answer 9

Hmmm

Answer 10

some combinations/permutations are missing some how

how do I know below permutation is not valid ?
4 4 2 0 0

It is not valid, Is there any general method to prune them out ?

Answer 11

each team plays 4 games...

Answer 12

So more than 1 team cannot win all 4 games

Answer 13

total wins is 10 and total loses is 10

Answer 14

SUM w = 10
SUM L = 10

Answer 15

each team w <= 4, : <= 4

Answer 16

requires more constraining

Answer 17

Okay, so here is my plan.... The number of wins for team \(i\) will be \(w_i\).

Answer 18

I am following

Answer 19

\[
\sum_iw_i = 10
\]

Answer 20

If we can distribute the wins, then loses will be determined by that.

Answer 21

Yes I got that !

Answer 22

We can't have 4+4+2+0 or 4+4+0+0 like you said...

Answer 23

however both are different cases

4 + 4 + 0 + 0 is easy to prune out as the sum is not 10

Answer 24

We could sort the teams by the number of wins, and then find permutations after the fact

Answer 25

4 3 _ _ _

Answer 26

remaining teams must add up to 10-4-3 = 3

Answer 27

will there be some invalid permutations ?

Answer 28

4 3 3 0 0

I think it is invalid

Answer 29

somehow i feel helpless identifying the pattern :/

Answer 30

I'm not sure if there is a simple solution to this, actually

Answer 31

Hmmm, ignoring scores for a second, the total number of match ups would be...

Answer 32

I think 4 3 3 0 0 is invalid.

Answer 33

The first team never loses. The second team can only lose to the first team. The third team can only lose to the first team. Does the third team win or lose to the second team?

Answer 34

I tried to create a simulation, but it would take almost a day to run it on 5 teams.
http://jsfiddle.net/wio_dude/9Lebe/25/
It doesn't take long with 4 teams though. I wonder if there is any insight to be found from it.