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n-group win

n-group win

Posers and Puzzles

F

Joined
11 Nov 05
Moves
43938
Clock
22 Jun 07
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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)?

Aiko

Joined
23 Mar 04
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254986
Clock
22 Jun 07
2 edits
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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.

m

Joined
07 Sep 05
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35068
Clock
22 Jun 07
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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.

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