I count 561. If you want the number of unique trips that visit each island once, thats 34!, or 2.95e38. If you want the number of edges in a complete undirecte

I count 561. If you want the number of unique trips that visit each island once, thats 34!, or 2.95e38. If you want the number of edges in a complete undirected graph, that's (34*(34-1))/2, or 561. Maybe when you account for currents the route from one atoll to another might be different than the same trip in reverse. If so there could be 1122 paths.