$\underline{\text { Kaibhanov A.K. }}$

The auditorium has the shape of a regular hexagon with a side length of 3 meters. In each corner, there is a snore meter that determines the number of sleeping students within a distance of no more than 3 meters. How many sleeping students are there in the auditorium if the sum of the readings of the snore meters is 7?
![](https://cdn.mathpix.com/cropped/2024_05_06_eab8c6bbe58aee0b55b3g-04.jpg?height=389&width=437&top_left_y=77&top_left_x=799)

Each student is "seen" by 2, 3, or 6 snorometers (see fig). Therefore, 7 can be broken down into a sum of terms, each of which is 2, 3, or 6. It is easy to see that 7 can be represented as such a sum in only one way: \(7 = 3 + 2 + 2\). The number of terms is equal to the number of students.

## Answer

3 students.