Determining the state of a cube after one snapshot

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Determining the state of a cube after one snapshot

Postby gerth » Mon Dec 12, 2011 10:24 pm

Hey!
I am trying to figure out if it's possible to determine the state of a scrambled cube by observing only three sides (without seeing the remaining 3 sides)?
Let's say I can see the front, the right and the upper side of the cube. Shouldn't it be possible to calculate how the back, left and down side look like? My thought was, that it is not possible to change anything on the hidden sides without a resulting change in one of the visible 3 sides. At least I think that this is impossible. Has anyone ever thought about that or can tell me more about this topic? Or is there even an algorithm which is feasible to determine the hidden 3 sides?
Thanks!
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Re: Determining the state of a cube after one snapshot

Postby borginator2 » Mon Dec 12, 2011 10:44 pm

I would have thought that with any scrambled cube you can see the orientation of all corners bar one, and the orientation and position of all the edges bar 3. All the centres are fixed, and assuming that it's a standard non-picture 3x3, the centre rotations shouldn't matter.

Since all moves tend to move patterns of 3 or 4, I suspect that those 3 edges should prove the problem, although I suspect the other corner can be calculated.
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Re: Determining the state of a cube after one snapshot

Postby Zeotor » Tue Dec 13, 2011 2:05 am

I think that you could always figure out what all of the corners are.

borginator2 wrote:Since all moves tend to move patterns of 3 or 4, I suspect that those 3 edges should prove the problem, although I suspect the other corner can be calculated.

You're right; those edges would be a problem. If you do (R B)(M U M U M U2)(M' U M' U M' U2)(B' R') to a solved cube, this is what you get.
1.png
1.png (12.75 KiB) Viewed 499 times

Now, when you rotate the cube so that the other three sides are shown, this is what you see.
2.png
2.png (11.74 KiB) Viewed 499 times

The puzzle looks solved but it isn't.
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Re: Determining the state of a cube after one snapshot

Postby borginator2 » Tue Dec 13, 2011 8:00 am

Kudos, Zeotor, I've never seen a move combo that affected just 2 edges before. :D
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