Problem 9.2. During the first half of the year, lazy Pasha forced himself to solve math problems. Every day he solved no more than 10 problems, and if on any day he solved more than 7 problems, then for the next two days he solved no more than 5 problems per day. What is the maximum number of problems Pasha could solve in 7 consecutive days?
Answer: 52.

Solution. Suppose Pasha solved at least 8 tasks (but no more than 10) in one of the first five days, then in the next two days he solved no more than 5 tasks per day. Thus, in these three days, he solved no more than $20(10+5+5)$ tasks. If he solved 7 tasks each day, it would be more.

It turns out that in the first five days, Pasha solved no more than 35 tasks. It remains to note that in the last two days, he solved no more than 17 tasks (since he could not exceed the limit of 7 tasks on both days), and he could solve 17 tasks (7 tasks on the sixth day and 10 tasks on the seventh day).