Graph Algorithms · Superchallenge problem

A project's activities are arcs in a directed network from start event $1$ to finish event $6$: $1\to2{:}4, 1\to3{:}6, 2\to4{:}5, 3\to4{:}3, 3\to5{:}2, 4\to5{:}1, 4\to6{:}3, 5\to6{:}6$ (days). The critical path is the LONGEST route from event $1$ to event $6$. How many DIFFERENT routes achieve this critical (longest) length?