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Here's some of what people around the Joshternet have been publishing about this subject. Different websites, different perspectives, and a few more places to explore.

Josh Urban Davis (opens on the publisher’s site)

joshurbandavis.com

  1. Josh Urban Davis

    Gygès: 12 shared rings -- four each of height 1, 2 and 3 -- sit on a 6×6 board with no fixed owner. Each turn you must move a ring from your own front-most occupied row, in a path of orthogonal steps exactly as long as its height, turning when needed. Land on an empty space and your move is done; land on another ring and you choose -- bounce the moving ring onward using the encountered ring’s heig