Problem 6.3. In a new math textbook, there are a total of 91 problems. Yura started solving them in the mornings, beginning on September 6.

Every morning, starting from September 7, he solves one fewer problem than the previous morning (until the problems run out).

By the evening of September 8, Yura realized that there were still 46 problems left to solve in the textbook. On which day of September will he finish solving the textbook?
Answer: 12.

Solution. In the first 3 days, Yura solved $91-46=45$ problems. Let's say on September 7th, he solved $z$ problems, then on September 6th, he solved $(z+1)$ problems, and on September 8th, he solved $(z-1)$ problems. We get that $45=(z+1)+z+(z-1)=3 z$, from which $z=15$.

Since $91=16+15+14+13+12+11+10$, Yura will solve problems for exactly 7 days, from September 6th to September 12th.