Cube rearrangement dilemma

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Cube rearrangement dilemma

Postby bboop » Wed Oct 15, 2008 6:23 pm

My little girl just bought a cube and within half an hour had removed about 10 of the stickers then restuck them on again! The cube was unsovleved at the time and now we believe the random order is the unsolveabel random order. does there exist an unsovled pattern of the cube so we can put the stickers back on in the same places!? Please someone tell me there is cause I love my kids but I'm gonna kill her......haha
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Re: Cube rearrangement dilemma

Postby TomZ » Wed Oct 15, 2008 7:23 pm

The odds are against you.

There are about 4.3 * 10^19 combinations on a cube that can be solved.

If you were to arrange all stickers randomly, there would be 54! / (9!^6) or roughly 10^38 different places for the stickers to go.

Thus, there is a probability of 4.2533 * 10^-19 that a cube with randomly arranged stickers is solveable.

The odds if you only swap 10 stickers are ofcourse alot higher, but still very low.

Your best bet is to get some replacement stickers and resticker the whole thing. If you swap over the stickers again, it is just going to look horrible anyways.
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Re: Cube rearrangement dilemma

Postby bboop » Thu Oct 16, 2008 11:48 pm

Thanks very much for that. I dont suppose it matters that we have all the stickers. I kind of understand what you are saying but not quite. If it is too hard, I think this brand new shiny cube it destined for the bin!!!

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Re: Cube rearrangement dilemma

Postby OsyenVyeter » Fri Oct 17, 2008 5:18 am

Unsolveable patterns do indeed exist.  Dont throw away your cube.  Ive had a couple cubes where the stickers were dying and what Id reccomend is either one of 2 things.  6 bottles of cheap nail polish for frustrated mothers of destructive children so that the 'stickers' are replaceable.  or 2, my favorite.  You rip all the stickers off and etch in designs with a sharp knife.  My cube has +, -, square, X, O, and the last one is one where i make some thing that looks like # but more horizontal and vertical lines.  It makes for a great new toy.  Let me know how that works out for ya. 
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Re: Cube rearrangement dilemma

Postby blackwidowcd » Sat Oct 18, 2008 11:34 am

I would take it apart and put 2 layers together, then see how many pieces can be put correctly in the final layer. Then only a few stickers would need to be switched.
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