Problem 6.5. Cat Matroskin, Uncle Fyodor, Postman Pechkin, and Sharik sat down at a round table. In front of each of them was a plate with 15 sandwiches. Every minute, three of them ate a sandwich from their own plate, while the fourth ate a sandwich from their neighbor's plate. After 5 minutes of the meal, there were 8 sandwiches left in Uncle Fyodor's plate. What is the minimum number of sandwiches that could have remained on Cat Matroskin's plate?
# Answer: 7

Solution. We will call the sandwiches eaten from a neighbor's plate stolen. Note that in 5 minutes, exactly 5 sandwiches were stolen.

At the same time, 7 sandwiches disappeared from Uncle Fyodor's plate, of which he himself ate no more than 5, meaning that at least 2 were stolen. From this, it is clear that no more than 3 sandwiches were stolen from Matroskin's plate, that is, no more than 8 sandwiches in total disappeared from there. Therefore, at least 7 sandwiches remained.

Note that exactly 7 sandwiches could remain if Uncle Fyodor and Matroskin always ate sandwiches from their own plates, while Sharik sat between them and ate 2 sandwiches from Uncle Fyodor's plate and 3 sandwiches from Matroskin's plate.