Question 105
Let $\mathrm{C}_{1}, \mathrm{C}_{2}, \ldots \mathrm{C}_{\mathrm{n}}$ be circles of the same radius placed in the plane so that no two of them are tangent and so that there is always a path through the circles going from a point of one of them to another (in other words, the circles are connected). Denoting by $S$ the set of intersection points of the circles, show that $|S| \geqslant n$.