Problem 4. The students of a class are going on a mountain hike, one behind the other. When Andrei arrived at the cabin, half the number of students still on the trail were already in the cabin. Bianca arrived tenth after Andrei, and after her, there were half as many students left as those who had arrived before her at the cabin. How many students are in that class?
Solution. Let's assume that Andrei is at position $n$. Then there are $n-1$ students in front of him, and $2n-2$ students behind him. ...................... $1 \mathbf{p}$

Bianca is at position $n+10$. In front of her are $n+9$ students, and behind her are $\frac{n+9}{2}$ $2 \mathrm{p}$

The number of students, relative to Andrei, is $n+2n-2=3n-2$.

The number of students, relative to Bianca, is $n+10+\frac{n+9}{2}$.

We obtain the equation

$$
3n-2=n+10+\frac{n+9}{2}
$$

with the solution $n=11$.

The number of children is 31