Tournament Scheduling

[MitchC]

Hi All,

My friends and I get together fairly frequently to play Mario Kart 64 (the best of the Mario Kart games).
The problem with the game is that there is no way to create a tournament for more than 4 players.
So, I have been trying to come up with a way in Excel to determine who should play who.

Basically, the problem is as follows:

Given a set number of players and a set number of rounds that each player should play, how can we determine a schedule of who plays who such that:
1) All players play the same number of rounds
2) Each round has 4 players
3) The tournaments are randomized (i.e. I've been able to develop a way to do this that isn't randomized but then if the same players are playing in two different tournaments, they will get stuck playing against exactly the same people the second time)

Note: It is not required that each player play every other possible combination of players as this type of tournament would take too long.


I've attached a sample sheet of what I've come up with so far. Right now, I think I'm close to a solution but I can't figure out how to force each round to have 4 players.
Note that, the way the spreadsheet works is that once the tournament is generated, I would copy and paste values. Then, the blank cells would be where you fill in the position of each player while the zeros represent the players who aren't playing.

Thanks to all who help!
TournamentTest.xlsx

[djapigo]

Hey MitchC,

You've got a tough problem here...

Take a look at this website, maybe it will give you an idea and narrow down your tournament...

http://www.printyourbrackets.com/rou...-generator.php

Sorry, I wish I can help, but you've got a very complex problem, which I'm sure someone else here can help...

Here's a few things I could not get my mind around...
1. What you are looking for is a combination w/o repetition problem? In your example of 8 players, you are looking at =COMBIN(8,4) [ie 8 players in 4 spots without repetition] and this will give you 70 combinations...
2. Out of this 70, again, from your example, you want to limit to 16 rounds...
3. So, the trick now is with the 16 rounds, everyone has to have played the same number of games... this is where the tricky situation comes in...

Good luck, I'll be following your thread...

- Dennis