6.1. In the club, there are 9 people. Every day, some three of them went to the cafe together, while the others did not go to the cafe. After 360 days, it turned out that any two people from the club had been to the cafe together the same number of times. How many times?
Answer: 30

Solution. The total number of pairs of people in the circle is $9 \cdot 8 / 2=36$. Over 360 days, the cafe was visited by $360 \cdot 3$ pairs (since three new pairs are added each day). Since all pairs visited the cafe an equal number of times, this number is $360 \cdot 3 / 36=30$.