Question

A delivery network allows routes from Start (S) to End (E) through intermediate hubs A, B, C.
Allowed edges:
S→A, S→B, A→C, A→E, B→C, C→E.
A route cannot visit more than 3 nodes including S and E.
How many valid routes from S to E are possible?

Hint:

When route length is restricted, always filter paths by allowed depth before checking connectivity. This avoids counting valid-looking but over-length paths.

Answer 1

Correct Answer: 1

With at most \(3\) nodes allowed (S, one stop, E), only single-hop-through routes of the form S-to-hub-to-E are even eligible, so a direct look at each of the three hubs settles it. From S you can reach A or B directly, but not C (nothing points from S into C). Of those two, only A also has a direct link onward to E; B connects onward only to C, not to E, so a route through B can't finish in two steps. Adding a second intermediate stop, such as going through both A and C, would push the route to four nodes total, which the "\(3\) nodes including S and E" limit rules out immediately. That leaves exactly one route that fits every requirement: \(S\to A\to E\), so the number of valid routes is \(\boxed{1}\).