I was wondering how many different possible combinations are there for unlocking an Android phone. In order to do this, you have to choose a path from a graph:
The graph is not regular: the nodes at the corners are linked to 5 nodes only, the nodes at the sides are linked to 7 nodes and the central node is connected to every other.
The unlocking paths can have any length between 3 and 9. Is there a simple way to count the possibilities?