Count a shape's corners, minus its edges, plus its faces. The answer is always the same.
Take any convex polyhedron, a cube, a pyramid, a soccer-ball shape, and count its vertices (V), edges (E) and faces (F). Try computing V minus E plus F for a few different shapes before reading on.
Reveal the answer
It always equals 2. A cube has 8 vertices, 12 edges, 6 faces: 8 − 12 + 6 = 2. Euler described this formula in the 1750s; it turned out to be a deep topological invariant, and it changes in a predictable way for shapes with holes through them, like a donut.
— Leonhard Euler, Elementa Doctrinae Solidorum — Presented to the St. Petersburg Academy, 1750s