# Ribbon Cube



## Jokern (Jan 26, 2014)

Hello, I recently found the Ribbon Cube on Google Play. It looks like a normal cube (Google Image Search 'Ribbon Cube') but the moves does not affect face you are turning around, this also enables 1/8th of a full turn. The app uses the equivalent of qtm when counting moves, ie it it counts half a turn as 4 moves, this gives me an avg of about 90sec and 60 moves on the 2x2 (In the program I write about further down I use the "face turn metric" which enables all 42 moves).

At first this puzzle really messed with my brain, much because it moves so differently from a normal cube. But now i have found some easy commutators and solve it easily. I'm not really fast but I'm just happy I solved it with very little help from the internets. And I'm sure if you learned some algs, and got an physical version, which would be awesome! you can easily reduce the solve time to around 10 seconds without any problems.

The moves I allow are any twist around a face with between 1-7 stickers. This gives 42 different possible moves.
The cube has 23!/4!^6 = 1.35*10^14 different permutations, with more symmetries you can probably reduce this number by quite alot, if you wanna solve all positions.
The naive lower bound for gods number is then: log(23!/4!^6)/log(42) = 8.7

My frustration with this puzzle motivated me to write program that solved it optimally. I wrote it in java using an IDA* algorithm. It uses LookUpTables containing optimal solution lengths for solving opposite sides as a heuristic. It does about 1solve/5seconds. I have so far done a bit over 10000 solves (from random 25 move scrambles) with the following result:

Optimal Solution Length78910Scrambles5313947722830ratio0.5%14%77%8.3%
53 1394 7722 830
The ratio of the number of scrambles that give a optimal solution of the given length is coincidentally similar to the 2x2. This leads me to guesstimate that Gods number for the Ribbon Cube is 11.
The optimal lengths have smaller variance for the Ribbon Cube compared to the Rubiks 2x2 so Gods number might be 10, but anything other than that seems unlikely to me.

The 3x3 version should have 54!/(91^6*24) = 4.2*10^36 permutations, and 9*11 possible moves. Which gives the lower bound log(54!/(91^6*24))/log(99) = 18.35.

Now to some questions: Has anyone calculated the actual God's number for this puzzle? How many symmetries does it have? Will the 3x3 have the same Gods number as Rubiks? Can you solve it? Have you tried it? You should!


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