I had a probability test and that was one of the questions:
We have an infinite grid of hexagons like this:
Each edge has a length of 1 and all the degrees are 120°.
There's a particle in one of the vertices and each second it randomly moves to one of it's neighbours.
After n seconds what is the expected distance squared of the particle from it's starting position?
I spent a lot of time on that but I really have no idea how to even approached this question.