CareerCup

Trick question. Given an odd number of teams, each team can't play only once a week.

Answer is 5.
Formulating: It is clear that only two matches can be held per week. And these two matches are played by 4 different teams. Now our task is to pick 4 teams out of 5. This can be done in 5C4 ways. ie 5

Team e plays two away games in a row, but that's not ruled out

In which case, here's the schedule:
a b c d e
1 -1 2 -2 0 a v b & c v d
-1 2 -2 0 1 a v e & b v c
1 -2 0 -1 2 a v d & b v e
-1 0 1 2 -2 a v c & d v e
0 1 -2 -1 2 b v d & c v e

Man, it's easy hitting that submit button. Answer is 5 weeks, letters are teams, number is game played, positive means away, negative means home

Hey ppl,
I know this is not the place for it, but I have a question regd project/thesis for master's students. How important do people think it is in getting a job?
Thanks

They only asked how many weeks. So C(5,2) is 10 and each week there will be 2 games (4 teams can play, 1 idle). so 10/2=5 weeks. As for not playing at home in consecutive weeks, it should be easy to arrange since 1 team will be idle. So 5 weeks is the answer.

Here is one possible solution:
1 - Host; 0 - Away; - didn't play
Week A B C D E
I 1 0 1 0 - AvB & CvD
II 0 1 0 - 1 AvE & BvC
III - 0 1 1 0 BvD & CvE
IV 1 - 0 0 1 AvC & DvE
V 0 1 - 1 0 AvD & BvE

It's 5c2 combinations.

Nm. Actually it's 5c2/2 if 2 games allowed per week.

Here are the answer pairs:
AB, CD
BE, DA
AC, ED
CE, DB
EA, BC

1 2 3 4 5
1 x x week3 week5 x
2 week1 x x x week3
3 x week2 x x week5
4 x week4 week1 x x
5 week4 x x week2 x

12,34 - 1 Home game
13,24 - 2 Home game
23,14 - 3 Home game
34,15 - 4 Home game
45 - 5 Home game
25 - 5 has to play next week cause last one is their home game and haven't played with 2 before.

Total - 6