E Finding the shortest path through a product wheel

Figure E.1 can be used find the shortest path from A to A through the product wheel. The five product graph requires us to solve all four graphs concurrently; make one move on each graph in turn, the first one to complete will be the shortest path (if more than one graph completes in a round, select the shortest one).

Figure E.1: Directed acylic graphs for solving the product wheel problem