Problem 6.2. Arkady, Boris, Vera, Galia, Dan, and Egor formed a circle.

- Dan stood next to Vera, to her right,
- Galia stood opposite Egor
- Egor stood next to Dan,
- Arkady and Galia did not want to stand next to each other.

Who stands next to Boris
Answer: Arkady and Galya.

Solution. From the first and third statements, it follows that Vera, Dan, and Egor stand in exactly that order counterclockwise. Since there are six people in the circle, Galya stands to the left of Vera, opposite Egor. The remaining people are Arkady and Boris. Since Arkady and Galya do not stand next to each other, to the left of Galya stands Boris, and to the left of Boris stands Arkady. The arrangement is as follows:

Boris

Galya

Arkady

Vera $\quad$ Egor

Dan

Next to Boris - Arkady and Galya.