A certain group of $n$ boxers is totally ordered by strength; if boxer $X$ is stronger than boxer $Y$, then $X$ wins every single fight against $Y$. The ordering itself is not known to us, and we do not have the slightest idea which boxers are stronger than other boxers.
Unfortunately, these boxers are also very moody; as soon as a boxer has lost a total of six fights in a tournament, he is disappointed and walks home right away (independently of the number of fights that he has won up to that point).
Our task is to organize a sequence of fights in a tournament so that in the end we exactly know the ordering of all $n$ boxers (and hence know for each pair, which of the two is the stronger one).
Question: What is the maximum number $n$ of boxers for which we can settle our task with absolute certainty?