Supppose you want to organize a tournament for $n$ players split into a number of groups $g$.

You also have a fixed number of players $m$ per group.

The competition is split into a number of rounds $r$.

The situation in which two players are in the same group more than once is called an error. (If players are in the same group say 3 times you have 2 errors).

The goal is to minimise the number of errors for given $n$, $m$ and $r$, or find the maximum $r$ for given $n$ and $m$ without errors.

I currently know that there are certain $n$ for which the number of errors is 0. But I could not find a formula for these $n$ at arbitrary size.

Is there a way to find a function for these numbers or do you know in which field this topic would belong?

I would also like to find an algorithm to minimize the number of cases or be able to estimate/calculate the minimal number of errors.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.