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The Super-CUBI puzzle box takes 324 steps to open or close it, instructions. And uses a Trinary System. It must have a solution as it would be hard to remember all the steps to take to open it. But what is it ?

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    $\begingroup$ I'm very, very jealous if you have this thing. $\endgroup$ – Gracelyn Rioux May 17 '15 at 14:41
  • $\begingroup$ I was very lucky to get the super cubi but the king cubi is the one I would like to have, 1536 steps Quaternary system used. $\endgroup$ – Tom May 17 '15 at 17:26
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As you have said, the Super Cubi requires 324 moves to be opened. The correct sequence is listed here:
enter image description here

In each step, you have to move one of the six faces. The numbers in the table represent the centimeters of translations. For example, 000022 means that faces #1 and #2 were moved by 2cm.

But how do you remember that sequence?
As you can see, in the first vertical half of the table the face #6 is always 0, while in the second half is always 1 (except for the last move). The face #5 is 0 for the first and last column, 1 for the second and fifth, 2 for the third and fourth. We can find similar patterns for all the faces.
Let's define "bounce" a move that follows the cycle [1,2,3,3,2,1]. When you apply the bounce move to a face in a certain status, the next status is determined by the next number in the above cycle. For example, if you bounce from 2 (and the previous status was 1), the next status will be 3.
Now a general rule to remember the moves (needs some practice, though):

  1. Face #1 oscillates between 0 and 2 every two moves (starting from 2).
  2. Face #2 bounces every two moves.
  3. Face #3 bounces every six moves.
  4. Face #4 bounces every 18 moves.
  5. Face #5 bounces every 54 moves.
  6. Face #6 bounces every 162 moves.

As you can see, the bounce distances increase with a factor x3 between two consecutive faces.

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    $\begingroup$ I believe the question is:what is the system or theory that governs this sequence of moves, so that you don't just memorize 324 steps but you know a rule like "move odd numbers inward" or "switch largest and smallest numbers" or whatever. I don't see this answer covering that at all $\endgroup$ – Kate Gregory May 17 '15 at 15:05
  • $\begingroup$ @KateGregory Good point! I'll add more details in my answer asap $\endgroup$ – leoll2 May 17 '15 at 15:08
  • $\begingroup$ @KateGregory Yes, its the system behind it or formula. As you only have to remember which step you are on, apply the formula so you do not $\endgroup$ – Tom May 17 '15 at 17:14
  • $\begingroup$ The sequence is the ternary Gray code. en.wikipedia.org/wiki/Gray_code $\endgroup$ – Jaap Scherphuis Apr 21 '16 at 15:19

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