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How do you calculate all the possible combinations on a Rubik's cube? 
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#1
Jun2314, 09:02 PM

P: 44

I thought it would just be the number of faces multiplied by the nine cubes on each face? What am i doing wrong?



#2
Jun2314, 09:18 PM

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#3
Jun2314, 09:29 PM

P: 44

I know very little programming, a tiny but if Python but that's about it



#4
Jun2314, 09:37 PM

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P: 15,166

How do you calculate all the possible combinations on a Rubik's cube?
You're not going to be able to count the permutations on a computer. The number is too big.
If you consider the problem of the number of permutations that can be made by pulling a Rubik's cube apart piece by piece and then reassembling it, this is a huge number. There are eight corner cubes which can be placed. That means 8! permutations just based on corner cube location. Each corner cube can be placed in one of three orientations. That's a factor of 3^{8} permutations on top of the 8! location permutations. The twelve corner cubes lead to two more factors, 12! and 2^{12}. Altogether, there are ##8! \, 3^8 \, 12! \, 2^{12}## permutations of the ripped apart and resembled cube. That is a *big* number. Most of these permutations do not lead to the nice all colors on one face arrangement. There are constraints, but the final number is still huge. 


#5
Jun2414, 01:09 AM

HW Helper
P: 2,264

See here
http://en.wikipedia.org/wiki/Rubik%27s_Cube There are $${8! \times 3^7 \times (12!/2) \times 2^{11}} = 43,252,003,274,489,856,000 \\ {8! \times 3^8 \times 12! \times 2^{12}} = 519,024,039,293,878,272,000. $$ combinations the larger number is 12 times the smaller as there are 12 orbits that is any position can reach 1/12 positions though legal moves separating possible moves into 12 orbits 


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