Lesson 2

Problem. Every pair of the seven teams played each other, and each game had a winner (no draws). When summarizing the tournament results, you naturally want to order the teams so that the first team defeated the second, the second defeated the third, and so on. To your surprise, you find that there are multiple such orderings. It turns out there can be quite a lot.

Construct a tournament on seven vertices where there are at least \(150\) such orderings. As an answer, enter a string listing the results of all games separated by spaces. We assume the teams are numbered from zero to six. For example, if there were three teams and they won against each other cyclically, it would be recorded as: \(\texttt{0 2 2 1 1 0}\).

(If you cannot construct it, study the following theorem and return to this step.)