ISF Logo   IS Forum
Forum Index Register Members List Events Mark Forums Read Help

Go Back   International Skeptics Forum » General Topics » Science, Mathematics, Medicine, and Technology
 


Welcome to the International Skeptics Forum, where we discuss skepticism, critical thinking, the paranormal and science in a friendly but lively way. You are currently viewing the forum as a guest, which means you are missing out on discussing matters that are of interest to you. Please consider registering so you can gain full use of the forum features and interact with other Members. Registration is simple, fast and free! Click here to register today.
Tags Rubik's Cubes

Reply
Old 12th March 2019, 02:06 AM   #41
TheGnome
Thinker
 
Join Date: Jul 2009
Location: Bern, Switzerland
Posts: 170
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.
TheGnome is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 12th March 2019, 02:23 AM   #42
Worm
Master Poster
 
Worm's Avatar
 
Join Date: Jun 2006
Location: Dundee
Posts: 2,553
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.
__________________
"Violence is the last refuge of the incompetent" Isaac Asimov

Not all cults are bad - I've joined a cult of niceness
Worm is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 12th March 2019, 03:29 AM   #43
Dave Rogers
Bandaged ice that stampedes inexpensively through a scribbled morning waving necessary ankles
 
Dave Rogers's Avatar
 
Join Date: Jan 2007
Location: Cair Paravel, according to XKCD
Posts: 28,609
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
__________________
Me: So what you're saying is that, if the load carrying ability of the lower structure is reduced to the point where it can no longer support the load above it, it will collapse without a jolt, right?

Tony Szamboti: That is right
Dave Rogers is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 12th March 2019, 04:18 AM   #44
P.J. Denyer
Philosopher
 
Join Date: Aug 2008
Posts: 5,159
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.
__________________
"I know my brain cannot tell me what to think." - Scorpion

"Nebulous means Nebulous" - Adam Hills
P.J. Denyer is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 12th March 2019, 05:11 PM   #45
arthwollipot
Observer of Phenomena
 
arthwollipot's Avatar
 
Join Date: Feb 2005
Location: Location, Location
Posts: 60,787
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.
arthwollipot is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old Yesterday, 03:56 PM   #46
Minoosh
Philosopher
 
Minoosh's Avatar
 
Join Date: Jul 2011
Posts: 8,682
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.
Minoosh is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Reply

International Skeptics Forum » General Topics » Science, Mathematics, Medicine, and Technology

Bookmarks

Thread Tools

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Forum Jump


All times are GMT -7. The time now is 01:30 AM.
Powered by vBulletin. Copyright ©2000 - 2019, Jelsoft Enterprises Ltd.

This forum began as part of the James Randi Education Foundation (JREF). However, the forum now exists as
an independent entity with no affiliation with or endorsement by the JREF, including the section in reference to "JREF" topics.

Disclaimer: Messages posted in the Forum are solely the opinion of their authors.