# n-group win

FabianFnas
Posers and Puzzles 22 Jun '07 08:02
1. 22 Jun '07 08:02
I've noticed that in a 4-man group tournament (here at RHP), if I get 4 wins, 12 points, then my group win is secure.

Queston 1: Is this true? Is 12 points enough togarantuee a win in this group?

Qustion 2: Is there any formula that could be used for any n-man group to garantuee a win?

If G(4) = 12, then what is G(6), G(8), G(12), and finally G(n)?
2. Aiko
Nearing 200000...!
22 Jun '07 08:432 edits
With a group out of four, you've played six games, winning four and losing two. Imaging you lose both games to opponent A. If opponent A wins all games so winning six, you're out of the game. Even winning that one game against opponent A but losing the second game to opponent B or C, will make opponent A go through.
3. 22 Jun '07 10:46
As a general rule, you can only afford to draw one match (winning all others) to guarantee a clear win. Drawing two, or losing one (winning all others) will guarantee a share of first place.

In a group of size N you play 2(N-1) games. So 3[2(N-1) - 2] + 2 = 6N - 10 will definitely send you through, and you need 6N - 8 to win outright.

At the other extreme, if everybody draws every game, then you can feasibly go through with 2N - 2 points, and you can be clear first with 2N.