A polyhedron has 20 triangular faces. How many edges does it have? How many vertices?
Let $X$ be the number of pairs $(a, f)$ where $a$ is an edge of $f$. We have $|X|=20 \times 3=60$. On the other hand, since an edge belongs to two faces, we have $|X|=2 A$ where $A$ is the number of edges, so $A=30$.

Since $S-A+F=2$ where $S$ is the number of vertices and $F$ is the number of faces, we have $S=12$.