6. Ms. Olga Ivanovna, the class teacher of 5B, is staging a "Mathematical Ballet." She wants to arrange the boys and girls so that exactly 2 boys are 5 meters away from each girl. What is the maximum number of girls that can participate in the ballet if it is known that 5 boys are participating?
Answer: 20 girls.

Solution: Let's select and fix two arbitrary boys - $\mathrm{M}_{1}$ and $\mathrm{M}_{2}$. Suppose they are 5 m away from some girl - G. Then $\mathrm{M}_{1}, \mathrm{M}_{2}$, and G form an isosceles triangle with the legs being 5 m. Given the fixed positions of $\mathrm{M}_{1}$ and $\mathrm{M}_{2}$, there can be no more than two such triangles (a diagram would be helpful here!). Therefore, for any pair of boys, there can be no more than two girls. The total number of pairs of boys is $C_{5}^{2}=10$, from which we obtain the upper bound.

It is not difficult to show that this bound is achievable - simply by placing the boys in a row with an interval of 1 m and constructing all possible isosceles triangles (their vertices will obviously be different).