Problem 4.6. Three two-person desks are placed one behind the other, and at these desks sit Artyom, Borya, Vova, Grisha, Dima, and Zhenya. There are no other students in the class. It is known that:

- Dima constantly distracts the student sitting in front of him;
- Borya looks at the back of Zhenya's head;
- Artyom and Grisha are close friends and sit at the same desk;
- the teacher has forbidden Vova and Zhenya from sitting at the same desk.

Who sits at the second desk?

![](https://cdn.mathpix.com/cropped/2024_05_06_f0908ee0d2b34517d87eg-4.jpg?height=491&width=525&top_left_y=374&top_left_x=464)
Answer: Zhena and Dima.

Solution. Let's see who can sit with Zhena at the same desk.

- Artem and Grisha sit together, so neither of them can sit with Zhena at the same desk.
- According to the problem, Borya sits behind Zhena, which means he is not at the same desk with her.
- Vova is not allowed to sit next to Zhena.

It turns out that the only one who can sit next to Zhena is Dima. But Dima cannot sit at the first desk, as there is a student in front of him whom he distracts; and Zhena cannot sit at the last desk, as Borya sits behind her. Therefore, Zhena and Dima sit at the second desk.