The vertices in the graph below are grain elevators, some of which can be connected by chutes to neighboring elevators, for the purpose of shifting grain from one location to another. The edges are directed because the chutes are inclined, to allow passage of grain by gravity in only one direction. Find a chute system that allows each elevator to be reached from the main elevator at vertex 1 with the shortest possible path. Is the solution unique? Do this problem by hand, rather than with Mathematica.

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