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A puzzle that is scrambled by just one move.
Irreversible Cube is based on an idea by Christoph Lohe:
"It is just a 2x2x2 Cube, however, with the following constrains:
- only clockwise quarter turns are allowed
- after a turn on one axis (out of three), the next move, if any, will need to be done on another axis
Obviously, it is not a normal twisty puzzle as you cannot simply reverse your move sequence. It also means: the puzzle is already scrambled after a first single move from the solved state."
So if we encode
"U" = upper face 90 degrees clockwise
"F" = front face 90 degrees clockwise
"L" = left face 90 degrees clockwise
then one could legally turn e.g. "UFLUFLULUFLUFLUL" as all turns are clockwise and there are no two-same-turns-in-a-row. However, "FF" would be illegal and the second "F" move should be blocked.
Irreversible Cube exactly achieves Christoph Lohe's goal. There are only single clockwise quarter turns, and any second quarter turn is blocked, only to be unlocked when another face is turned 90-degrees clockwise.
Note that the puzzle has no easy undos. Once a quarter turn clockwise has been made, one cannot undo it by turning anti-clockwise. Anti-clockwise turns are blocked by the mechanism.
Analysing the mechanism, the follow steps happen when turning a face clockwise.
1) First the turning face locks itself against turning back to it original position. From this point, one can only move forward.
2) Next the turning face unlocks the previously locked adjacent face.
3) Then, the turning face locks itself against turning back to the adjacent-faces-unlocking state.
4) Finally, the turning face blocks. Now it can only be unlocked by turning an adjacent face.
Jaap Scherphuis found these facts about this puzzle:
- The number of states is the same like the normal 2x2x2 orbit size: 3,674,160
- Some states require 37 moves to solve! ("God's number")
- The shortest identity has length 14. It means after a first move from the solved state you will need 13 further moves, at least, to go back to the solved state.
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Thank you to the following people for their assistance in helping collect the information on this page: Andreas Nortmann, Jack Lieberman.
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