2. Seryozha decided to start eating properly and every day he ate one fewer chocolate cookie and one more sugar-free cookie than the previous day. In total, during the time of proper nutrition, he ate 264 chocolate cookies and 187 sugar-free cookies. How many days was Seryozha on a proper diet?
Answer: 11 days.

Solution 1. The total number of cookies eaten each day is the same. In total, Seryozha ate $264+187=451=11 \cdot 41$ cookies. Since the proper diet lasted more than one day and he ate more than one cookie each day, either he ate for 11 days, 41 cookies each day, or for 41 days, 11 cookies each day. But since the number of sugar-free cookies increased by 1 each day, in the second case, it would have exceeded 11 on one of the days. Therefore, this case is impossible.

Solution 2. If we "reverse" the sequence of the number of chocolate cookies, while leaving the sugar-free cookies unchanged, the total number of cookies will not change, but the difference between the number of chocolate cookies and sugar-free cookies eaten each day will become constant. Since $264-187=77=7 \cdot 11$, the proper diet lasted either 7, 11, or 77 days. Since the number of days is odd, the total number of cookies eaten is the product of the number of days and the number of cookies 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. Not justified why there cannot be a different number of days, 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 Seryozha could have eaten this way.