stiefels.net

I started this project because I was faced with the following problem:

Let’s say you want to plan a skat tournament with 12 players and you have four tables available. So three players are sitting on every table playing one round against each other. After a round the players are changing their seats so that no player is playing against an opponent he or she already played against.

The question now is: Can I arrange my players in a way so that every player is playing five times and not playing against an other player twice? And if so, how would this arrangment look like?

Technorati Tags: combination, skat tournament

The Program

If you try to find a solution with a pen and a sheet of paper without using higher mathematics you’ll see that finding an answer isn’t quite trivial. There are about 370,000 (!) possible arrangements just for the first round. So trying to find a solution by hand is impossible.

This project is about a program which brute-forces all possible combinations and tries to find a five-round-tournament. But, going through ALL possible combinations though would take several hundred years (!). A mathematician told me, that there is a thing, they call without loss of generality which says that I can preselect any combination for the first two rounds and if there is a five-round-solution it will occur anyway. Preselecting the first two rounds the total calculation time shrinks down to just a few seconds.

The Solution

Well, according to the output of my program there is no five-round-solution, unfortunately. But there are may four-round-solutions and even some three-round-solutions.

You can have a look at the project site where you can find a download link and a short manual how to use the tool. The tool can also be used to find possible tournament arrangements for other scenarios than 12 players and four tables.