Hi, kind of random, but I am trying to design a preset matrix for running a pinball tournament. Not sure if anyone here would be able to advise me on this, but any thoughts or references would be appreciated. Essentially, I want to construct a design with the following conditions:
1) The tournament consists of 9 rounds. 2) Each round consists of 4-player games. 3) Each 4-player game is played on one pinball machine.
Now the hard part... 4) Players only play each other once. 5) No player plays the same machine twice.
I thought this may have been possible by taking four latin squares, stacking them on one another, then designating the cells as machines, the columns as rounds, and the rows as players. This solved the problem of each player playing each machine once. It also provided four players per match. I could also use any size latin square and simply keep the first 9 columns to supply nine rounds. However, some players still randomly faced each other twice! I can't figure any way around this (and there may not be one). I am not a computer programmer or a great mathematician, but I did find this paper providing a set of 4 mutually orthogonal latin squares of the order 9 (D. A. Drake and W. Myrvold, 2004). Except, it still didn't prevent any two given squares from repeating a sequence, it just eliminated the possibility of the same 4 players facing off again (which IS progress, I suppose). Anyhow, I have turned to this forum as a last hope! Please don't flame me :)
Thanks in advance, Fred
P.S. If you like pinball and live in the NW you should come to the tournament!
http://crazyflipperfingers.com/talk/viewtopic.php?f=9&t=865