This is Simon’s remix of a video by James Grime about the same subject on the SingingBanana math channel: https://www.youtube.com/watch?v=ODtwehGzoLM

The Utilities Problem is a problem about connecting three houses to three utility companies of which every company provides three services (water, gas, electricity) so that no lines cross.

Simon proves the problem impossible by contradiction (by assuming it’s possible and applying Euler’s Formula about 3D Solids to the solution).