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Patience Puzzle Solution

This page shows the steps in solving the patience puzzle.
(also known as the "Chinese rings" or "Cardan's rings".)


This puzzle is sold at gift and novelty shops.
STOP READING NOW IF YOU DON"T WANT ME TO GIVE AWAY THE ANSWER!
If you've pulled your hair out already and you want the answer read on.....
Starting with the blue bar on the last stem the object is to remove the blue bar.
(or to put it back on the last stem if you are starting with it off.)
When I first learned to work this puzzle I was amazed that my hands
seemed to do it without me consciously thinking about it.
I could work the puzzle but I couldn't describe the sequence.
One day it finally dawned on me that...

the puzzle is a binary Gray code!

(in particular... it's reflective Gray code)
This is my first attempt at programming with javascript.
I had as much fun writting this page as I did solving the puzzle.