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Tags Rubik's Cubes

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Old 12th March 2019, 02:06 AM   #41
TheGnome
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Originally Posted by Dave Rogers View Post
FTFY.



It's possible, if I recall correctly, to reverse the orientation of any two side cubes without changing anything else; there are therefore two possible arrangements of the side cubes that are not equivalent. Similarly it is possible to rotate any two corner cubes in opposite directions without changing anything else, so in effect there are only three possible arrangements of the corner cubes that are not equivalent. Multiplying those together indicates that, if you take a cube apart and then reassemble it completely randomly, there is a 1/6 probability that this will result in a soluble cube.

I bet you all wanted to know that.

Dave
I see someone is wrong on the internet (at least I think so), and on a subject of such immense importance.

There actually are 12 different orbits (or universes or whatever) so this probability would be 1/12.

Just trust me, I know what I'm doing wikipedia knows best.
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Old 12th March 2019, 02:23 AM   #42
Worm
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Originally Posted by pgwenthold View Post
The dumbest thing about it was that he "broke the record" for the fastest time to solve three Rubik's cubes while juggling them, which means that...someone had already done it, albeit in a slower time.

Then again, it may have been his own record that he broke.
I'm not sure that's necessarily true. I was listening to something last week where they were talking about people who had been described as 'broken a record' when in fact all they had done was beat a target set by the Guinness World Record people, because nobody else had done it before. It was all stupid stuff to do with arranging things with chopsticks - it might have been on No Such Thing As A Fish.

Originally Posted by arthwollipot View Post
Douglas Hofstadter devoted two whole chapters to the Cube in his book Metamagical Themas. If you want serious full-on cube nerdery, I suggest picking up a copy.
I strongly suggest picking up a copy if you have even a passing interest in puzzles, maths or logic. It's a fantastic book.
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Old 12th March 2019, 03:29 AM   #43
Dave Rogers
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Originally Posted by TheGnome View Post
I see someone is wrong on the internet (at least I think so), and on a subject of such immense importance.

There actually are 12 different orbits (or universes or whatever) so this probability would be 1/12.

Just trust me, I know what I'm doing wikipedia knows best.
Ah yes, you're right; any two corners can be rotated separately so there are (3x2) corner possibilities multiplied by 2 edge possibilities. Missed that.

Dave
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Old 12th March 2019, 04:18 AM   #44
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Originally Posted by BowlOfRed View Post
In both cases, as long as you reassemble/resticker to a solved cube at the end, you're fine. If you put it back randomly, it may not be possible to solve just by twisting.
This was the point I was going to make. To give a nice easy situation to imagine, think about the corner pieces where a single piece has three colours on it, if you swap.one colour with that from the opposite face of the cube you've created a piece that cannot be correctly positioned anywhere on the puzzle even if you took it apart and reassembled it.
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Old 12th March 2019, 05:11 PM   #45
arthwollipot
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Originally Posted by Worm View Post
I strongly suggest picking up a copy if you have even a passing interest in puzzles, maths or logic. It's a fantastic book.
It certainly is, Worm. There are few books about which I can honestly say that they changed my life. This is one of them.
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Old 18th March 2019, 03:56 PM   #46
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Originally Posted by WhatRoughBeast View Post
Sorry, no. Please reread my answer. In the case I gave, the blue face is fixed to the red by 3 pieces which share red and blue. Therefore, any solution must have red and blue adjacent, and red and blue can never be on opposite faces.
By "solved" I meant, making all the cube faces a solid color. I wasn't really thinking about the edges.

IRL, white is opposite yellow, red is opposite orange and blue is opposite green. No solution of a factory cube will give you yellow and white adjacent, but if someone re-stickered the faces to pin white to yellow, the cube would still be solvable in that sense.

I finally did the thing. Will probably let a kid re-scramble it.
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Old 19th March 2019, 12:23 PM   #47
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Not a bump. Just wondering about another question. In the simulated cube on Google's website, the middle layer rotates as well. Nothing in the algorithms I saw (beginners) has any rotation of the middle. You can rotate it, but the only effect is breaking all the solved faces. However, white is still opposite yellow etc., so the cube's integrity is unaffected.

This seemed counterintuitive to me, but then my mathematical intuition isn't very sophisticated.

I was wondering if anyone else had experience with the Google cube. After a while the ability to spin faces seems to expire and all I can do is rotate. If I call it up in a new page (on an iPhone) I can do full manipulation. I avoid spinning the middle. In another counterintuitive (to me) bit, I was able to visualize better than with the physical cube. I think it's because rotating is kind of a pain and I'm forced to think about the pairing of opposite sides. I can think of a certain face being "on the yellow side" instead of "at the bottom." Or maybe I'm just more experienced? Has anyone tried the virtual cube?
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Old 19th March 2019, 12:56 PM   #48
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Originally Posted by theprestige View Post
Apparently the method is a simple sequence of rote gestures.
At the risk of continuing a conversation no one else cares about (o, the ignominy), what else could it possibly be? You have to cast a spell over it, or something? If it's solvable at all, yes, it's due to certain "rote gestures," aka algorithms. If you're a beginner who is spatially challenged (me), you can find algorithms for dummies. This involves simpler sequences of moves, but more total moves (twists). It has been proven that if you have sufficient information processing capacity at hand, any cube can be solved with 20 twists:

God's number is 20

Quote:
There are many different algorithms, varying in complexity and number of moves required, but those that can be memorized by a mortal typically require more than forty moves.
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Old 19th March 2019, 10:00 PM   #49
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I've never heard of "the google cube", and I don't think I found the right thing when I tried to...well...google it.
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Old 19th March 2019, 10:41 PM   #50
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Originally Posted by BowlOfRed View Post
I've never heard of "the google cube", and I don't think I found the right thing when I tried to...well...google it.
Thanks for answering, I really appreciate it.

Google's Rubik's Cube

Another cool website:

Ruwix.com
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Old 20th March 2019, 01:55 AM   #51
Dave Rogers
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Originally Posted by Minoosh View Post
Not a bump. Just wondering about another question. In the simulated cube on Google's website, the middle layer rotates as well. Nothing in the algorithms I saw (beginners) has any rotation of the middle. You can rotate it, but the only effect is breaking all the solved faces. However, white is still opposite yellow etc., so the cube's integrity is unaffected.
A rotation of the middle horizontal layer can be broken down into rotations of both top and bottom layer in the opposite direction, followed by a rotation of the whole cube. A rotation of either of the vertical middle layers is the same with a rotation of the whole cube before and after to bring the middle layer to the horizontal then back to the vertical. Since rotation of the whole cube has no effect on its configuration, any rotation of the middle layer is therefore equivalent to rotating the two faces on either side of it in the opposite direction.

Dave
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Old 20th March 2019, 08:58 AM   #52
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Ah, I had come across the doodle, but I didn't see the instructions the first time. Now I understand how to interact with it.

And Dave has answered what middle slice moves mean. Only the relative motion of the slices matter, so most solutions assume you're not rotating the entire cube.
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