1. Nезнayka, Doctor Pilulkin, Knopochka, Vintik, and Znayka participated in a math competition. Each problem in the competition was solved by exactly four of them. Znayka solved strictly more than each of the others - 10 problems, while Nезнayka solved strictly fewer than each of the others - 6 problems. How many problems were there in the math competition?
Answer: 10.

Each of Dr. Pill, Knopochka, and Vintik, according to the condition, solved from 7 to 9 problems. Therefore, the total number of solved problems ranges from $10+6+3 \cdot 7=37$ to $10+6+3 \cdot 9=43$. Note that this number should be equal to four times the number of problems. Among the numbers from 37 to 43, only one is divisible by 4 - this number is 40. Therefore, the total number of solved problems is 40, and the total number of problems was 10.

## Criteria

+ Correct solution - 7 points.

$\mp$ Correct answer without explanations (or with incorrect explanations) - 2 points.