Kaiibhanov A.K:

The audience has the shape of a regular hexagon with a side of 3 m. In each corner, a snoremeter is installed, determining the number of sleeping students at a distance not exceeding 3 m. How many sleeping students are there in total in the audience, if the sum of the snoremeter readings is 7?

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![](https://cdn.mathpix.com/cropped/2024_05_06_d69082500b56170eb8ddg-18.jpg?height=397&width=446&top_left_y=2254&top_left_x=795)

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 equal to 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.

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