Hints for the Amida-kuji Problem

Here are some questions that might help you fully understand how amida-kuji works.

-  Can you find a general pattern for reversing the order of players, so that players 1, 2, ..., n go in the order n, ..., 2, 1?

-  Can you find a general pattern for reversing a single pair of players, so that players go in the order ?

-  Imagine that the players all travel through the network at once.  If you keep track of what players meet as they travel across each vertical line, is there any need to have the same two players meet twice?