There are three equal-radius, tangent circles. What is the area of the lobe between the circles if the radius of each circle is $r$?
The centers of the circles form an equilateral triangle, each side of which is $2 r$, so its area is $r^{2} \sqrt{3}$. The desired area is obtained by subtracting the area of the 3 circular segments from the area of the triangle; thus

$$
t=r^{2} \sqrt{3}-\frac{r^{2} \pi}{2}=r^{2}\left(\sqrt{3}-\frac{\pi}{2}\right)
$$

(Petrik Sarolta, Budapest.)

Number of solutions: 45.