2. Matvey decided to start eating properly and every day he ate one bun less and one pear more than the previous day. In total, during the time of proper nutrition, he ate 264 buns and 187 pears. How many days was Matvey on a proper diet?
Answer: 11 days.

Solution: If we "reverse" the sequence of the number of buns, while leaving the pears unchanged, the total number of buns and pears will not change, and the difference between the number of buns and pears eaten each day will become constant. Since $264-187=77=7 \cdot 11$, the correct diet lasted either 7, 11, or 77 days. Since the number of days is odd, the total number of buns and pears eaten is equal to the product of the number of days and the number of buns and pears eaten on the middle day. But 264 is not divisible by 7, so the number of days cannot be 7 or 77.

Criteria: Full solution - 7 points. If the reason why there cannot be a different number of days is not justified, but the rest is correct - 5 points. Only the answer - 1 point. The problem assumes that the event has already occurred, so the student is not required to provide an example of how Matvey could have eaten this way.