Giving intersecting areas a different symbology?

Hi Folks

Is this one possible?

I have a layer of polygons (which are actually buffers but think that is irrelevant), and some of them overlap.

What I would like to do is to be able to symbolise the areas where they overlap in a different colour/style. However, to be extra complicated, in some areas more than a couple of polygons overlap, so there maybe areas where there is an intersection of 2/3/4 polygons.

Ideally, I would like to be able to symbolise these areas so it shows how many polygons are intersecting.

I hope that makes sense, and there is some sort of query I can run to do this!

Thanks