CareerCup

Yes, of course. This is clear. I need solving this at day time, not at 3AM in the morning :) 11 is the answer here

Look at this situation below. 1st 5 teams split 11 wins each (11 * 5 = 55)
Total is 56 wins. In that situation, you do need 12 wins to guarantee to get through.
Just put that in Excel. So wfchiang is correct I take my words back - 12 wins is the answer

Team No Wins
1       11
2 11
3 11
4 11
5 11
6 0
7 0
8 0

I meant "4 teams having 8 wins and 4 teams having 6 wins"

wfchiang - it is incorrect even when you think intuitively - no disrespect though.
Answer = 8 games.
Total games played: 8 teams * 14 games = 112 games
Games won: 112/2 = 56 games (because when one team wins, other loses - assuming no ties)
What is the most competitive situation case: 56 games/8 teams = 7 games won by each team.
So when all teams win 7 games each, it means they all have equal place.
To get to 1st place, it must be 8, but other team win should be diminished to 6
To get into 2 winning teams, it again must be 8, making 2 other teams win =6 and so forth, until we have 4 teams having 8 wins and 4 teams having 5 wins
So, in most competitive situation, you will need 8 wins to get through. If someone has better mathematical explanation, I will appreciate that