Re: Combinatoric Problem

On May 4, 12:20 pm, bill <b92...@xxxxxxxxx> wrote:
On May 4, 10:40 am, e_hobsb...@xxxxxxxxxxx wrote:

Hi,

I got a question regarding a real problem. I tried a bit to solve it
myself, but got stuck quite fast. Problem is:

Twelve collegues are out bowling. In each game, four opponents meet.
Everyone should play against everyone else in the same game at least
once. What is the minimum number of games you could play?

It sounds constructed, I know, but some collegeues really were out
bowling and started to discuss how to do this.

Any clues?

//Eric

There are 66 possible pairings and each game involves only three
pairings.
Thus at least 22 games must be played.

But this is not the minimum. It is impossible to have 66 unique
pairings in only 22 games. In order to determine how many additional
games are required, you would probably have to revert to a "brute
force" approach.

Bill J

Sorry, there are 6 pairings in each game, not 3.

.

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