Problem 3. Vasya solved problems for 15 days - at least one problem each day. Each day (except the first), if the weather was cloudy, he solved one more problem than the previous day, and if it was sunny, one less problem. In the first 9 days, Vasya solved 13 problems.

a) What was the weather like on the 10th day? How many problems did he solve on that day?

$[4$ points]

b) What is the maximum number of problems Vasya could solve on the 15th day?

$[2$ points] (B. Frenkin)
Answer. a) The 10th day was cloudy, Vasya solved 2 problems; b) 7 problems.

Solution. a) See the solution to problem 2 for 6th grade (p. 4).

b) Since on the 10th day Vasya solved 2 problems (see part a), and in each subsequent day he can solve a maximum of 1 more problem, then in 5 days he can solve a maximum of $2+5=7$ problems. This will happen if the weather was cloudy from the 11th to the 15th day.