20 players plays in four-player-matches

[hassehulabeck]

First of all, great thanks for this site and the incredible amount of help that Ian is doing.

Now to the problem. Again it is pinball. 20 players will compete against each other. I've managed to do a schedule that allows every player not to face another more than once, which was simple as they will be playing only five rounds (due to time aspects).

Each match between the four players will be played on three different pinball games. That means that player A, B, C and D will play against each other on game 1, 2 and 3.

The facility has some 20 + games, so there shouldn't be any problems, but I hit the wall, as I want every player not to play on one game more than once.

So, I have 20 players. I have five rounds, and every round is matchplay on three games, which means that every player will play on 15 pinball games. Is it possible to do this, or do I need to have some 30 or 40 games to make it happen?

Thanks for any help.

[Ian Wakeling]

I can't see any easy way of solving this problem.  I can see that there is quite a lot of flexibility, only 5 rounds and you have more pinball games than necessary - if I had the time do it, then the problem could most likely be solved by computer search.