Counting the number of paths traversing the nodes of the intersections of a binary tree with concentric circles Consider the following figure that could be described as the representation of a binary tree whose branches split on 5 concentric circles. It contains 63 knots. ![enter image description here]( How many related paths are there that link the 63 nodes using 62 "segments" belonging to the tree or the circles? An example of such path: ![enter image description here](

I could compute the solution thanks to nathey who pointed me to the Matrix Tree theorem. For those interested it's 2.019165124017958*10^28