# A discrete mathematics problem by Anthony Pham

**Discrete Mathematics**Level pending

An ant is on a regular tetrahedron, where all the edges are 1 meter long. The ant, starting on a vertex, randomly chooses and crawls to another vertex, and repeats. The probability that the ant is back to the same vertex after crawling 5 meters can be written as \(\frac{p}{q} \). If *p* and *q* are coprime, what is *p*+*q*?