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Google tells me that a standard 3x3x3 Rubik's Cube has 43,252,003,274,489,856,000 permutations. If I wanted to store data on that Rubik's Cube, how much could I store?

The only way I see to store data on a Rubik's Cube is to assign an integer to each permutation, then convert that integer into binary. It would take 66 bits to store an integer of that size, so the Cube could theoretically hold 65 bits of information by my calculations.

Is there any way to eke out more than 65 bits of storage from a Rubik's Cube?

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    $\begingroup$ This doesn't sound like a computer science question to me. The part that is a CS question, you've already answered. The answers I can come up with to what remains are non-CS answers, like "glue a USB pendrive to the Rubik's cube". What makes you think there is a CS angle to this? $\endgroup$
    – D.W.
    Jun 8, 2016 at 4:39
  • $\begingroup$ Where should I put it than? $\endgroup$
    – bakester14
    Jun 8, 2016 at 6:47
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    $\begingroup$ I think there's some CS content to add to an answer. Seems like a legitimate question to me. $\endgroup$ Jun 8, 2016 at 8:03
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    $\begingroup$ What's the most efficient coding-decoding scheme? That's a slightly more CS question. Note that some permutations may be isomorphic under rotation, so I wouldn't necessarily know which side is up if I got it in the mail, so you need an unambiguous encoding scheme. $\endgroup$ Jun 8, 2016 at 11:21
  • $\begingroup$ You can store 65 bits of information therotically but i think the bottleneck of the problem is that you will spend too much time at reading information,which means going from one state to another, simply solving the cube for each iteration of info. $\endgroup$ Jun 8, 2016 at 14:31

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If you consider the cube as living in a physical space, then you can get an extra factor of 24 from its orientation: assume it's sitting on a table and note the uppermost face (six options) and the face that's facing north (four more options). That gives you $\lfloor \log_2 (24\times 43\ 252\,...)\rfloor = 69\,\text{bits}$, and you could get even more by considering more fine-grained notions of orientation, at the risk of losing information by somebody jostling the cube.

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