Inspired by the three utilities puzzle from prog_SAHIL I'm now posting a similar puzzle that makes use of the topology of a cup with a handle:
The question is:
How many distinct points can you draw on the surface of this cup, such that it is possible to connect each point with all other points pairwise without any connections crossing each other (or one of the points)?
For example if you have 4 points the connections could look like this: