Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 4 / 21F / b / Solution

Choose a triangulation of the sphere having every branch point as a vertex. Its lift has twice every edge and face, and twice every nonbranch vertex, but only one vertex above each of the $n$ branch points. HenceSince $\chi ({\Sigma }_g)=2-2g$, this gives $n=2g+2$, the degree-two Riemann-Hurwitz formula.