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Joe Pellino
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 Re: Rubik's Cube   « Reply #25 on: Jan 9th, 2003, 6:20pm » Quote Modify Remove

I dont know exactly how to solve it but i do know that the fastest way takes 29 moves from any random position.
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Icarus
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 Re: Rubik's Cube   « Reply #26 on: Jan 10th, 2003, 2:34pm » Quote Modify

on Jan 9th, 2003, 6:20pm, Joe Pellino wrote:
 I dont know exactly how to solve it but i do know that the fastest way takes 29 moves from any random position.

Joe, can you tell us where this number comes from? Kozo's website mentions an upper bound of 29 moves, but it was counting half-turns as one move, whereas the rules Wu has set for us count half-turns as two moves. The quarter-turn only result on that website was 42.

I still seriously doubt that there are any positions more than 20-22 moves away from solved.
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biwema
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 Re: Rubik's Cube   « Reply #27 on: Mar 6th, 2003, 3:20pm » Quote Modify

Hi,

Normally a 180 degree turn is also considered as one move. In that case Kociemba's 'Cube Explorer' might be quite interesting:

http://home.t-online.de/home/kociemba/cube.htm

This tool should normally find a solution with less than 21 moves within a few seconds. If you want to prove its optimality, it needs some minutes for 17 moves or several hours for 20 moves.
There are starting positions that need 20 moves (including 180 degree moves) to solve. I don't know if there is a situation which need's more.
Nevertheless it is a funny tool to play with.

According to Mathworld, 29 moves are proven, but the real maximum might be lower.

biwema
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Icarus
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 Re: Rubik's Cube   « Reply #28 on: Mar 6th, 2003, 5:05pm » Quote Modify

"Normally" depends on who you are talking to and how they are viewing the problem. In terms of "ease of maneuver", a half-turn is barely any harder than a quarter-turn. But viewed from the point of view of "change of relative positions", clearly they are not equivalent. This latter approach is more intrinsic, while the former is geared towards a particular application.

The big problem is mixing numbers computed according to one definition with those computed by another.

Since William established this puzzle using the quarter-turn only definition, and since most of the numbers were computed using it, I strongly recommend sticking to it.

Using this definition, the best results here demonstrated or referenced in a reliable fashion are:

The maximum number of moves required by "God's Algorithm" is at least 20 (from my 3rd post) and at most 42 (the MathWorld result, expressed in quarter turns).
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I wonder: Which is larger
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commando
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 Re: Rubik's Cube   « Reply #29 on: May 8th, 2003, 11:39pm » Quote Modify

Pivotal for determining the minimum number of moves required is a special move called "The Superflip".
Jerry Bryan proved in 1995 that a minimum of 24 quarter turns (front, left, back, upper, right, bottom) are required to arrive at the superflip.
Mike Reid showed proved in 1998 that performing the superflip and then permuting the center faces (superflip + 4-spot) requires an additional two moves, bringing our minimum to 26.  This could be the "longest" move.

Some interesting places to look:

The superflip (with java cube!):
http://www.randelshofer.ch/rubik/patterns/U080.01.html

Michael Reid's homepage:
http://hedgehog.math.arizona.edu/~reid/Rubik/

More results (including the answer: God's algorithm is bounded between 26 and 42 moves, according to wu's rules):
http://www.geocities.com/jaapsch/puzzles/theory.htm
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Patrick Hines
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 Re: Rubik's Cube   « Reply #30 on: May 22nd, 2003, 10:10am » Quote Modify Remove

Hey, I'm 14 and i can do the rubiks cube no problem, but i just can't figure out what this riddle even means, i've been working on figuring out how to do the Rubiks Cube in the least amount of moves, than i found this. But this makes no sense to me . If you have time to email me back that would be great, in the mean time i'll just work more on trying to figure this out. See ya!
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Patrick Hines
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 Re: Rubik's Cube   « Reply #31 on: Jun 29th, 2003, 8:04pm » Quote Modify Remove

Hey, i was replying to Joe, the Rubiks Cube can be done in less than 29 moves, i don't know the guys name but he did all the math behind it and the least amount of moves you can do it in is 15, i have no clue how thats possible, but it is true, noone has ever done it in 15 moves, or at least not recorded.
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Icarus
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 Re: Rubik's Cube   « Reply #32 on: Jul 5th, 2003, 7:10pm » Quote Modify

Actually, T&B, in this post, I proved that the minimum number of quarter-turns has to be at least 20. According to the information provided by commando the minimum is at least 26.

Patrick - The last link commando provided counts the number of moves required to solve the "superflip" as 20 when you count half-turns as 1 move, so even by that method your 15 moves number is clearly too low.
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I wonder: Which is larger
When their digits are reversed? " - Anonymous
NetJay Says HI!
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 Solving Example   « Reply #33 on: Jan 12th, 2005, 3:15pm » Quote Modify Remove

http://www.mbsnet.dk/?loc=articles&show=26
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Icarus
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 Re: Rubik's Cube   « Reply #34 on: Jan 12th, 2005, 4:06pm » Quote Modify

Okay, towr, what does it say? (I'm very grateful that not everyone is as language-impaired as I am!)
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ThudnBlunder
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 Re: Rubik's Cube   « Reply #35 on: Jan 12th, 2005, 10:15pm » Quote Modify

on Jan 12th, 2005, 4:06pm, Icarus wrote:
 Okay, towr, what does it say?

It's probably double-Danish to him, too!
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towr
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 Re: Rubik's Cube   « Reply #36 on: Jan 13th, 2005, 12:28am » Quote Modify

Yeah, Dutch isn't exactly Danish.. Europe just isn't as uniform as the USA; we can't understand everyone just because they're in the same part of the continent
 « Last Edit: Jan 13th, 2005, 12:29am by towr » IP Logged

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Icarus
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 Re: Rubik's Cube   « Reply #37 on: Jan 13th, 2005, 2:54pm » Quote Modify

Well, obviously some of you can at least recognize what language it is.
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And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
towr
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 Re: Rubik's Cube   « Reply #38 on: Jan 13th, 2005, 11:39pm » Quote Modify

on Jan 13th, 2005, 2:54pm, Icarus wrote:
 Well, obviously some of you can at least recognize what language it is.

Or we recognize what 'dk' in the domainname stands for, Denmark.
If the exact same page had been in the domain
www.mbsnet.se, I'd have called it Swedish instead.
 « Last Edit: Jan 13th, 2005, 11:41pm by towr » IP Logged

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ThudnBlunder
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 Re: Rubik's Cube   « Reply #39 on: Jan 14th, 2005, 11:51pm » Quote Modify

on Jan 13th, 2005, 11:39pm, towr wrote:
 Or we recognize what 'dk' in the domainname stands for, Denmark.   If the exact same page had been in the domain   www.mbsnet.se, I'd have called it Swedish instead.

I also checked a couple of words with an online translator.
When correcting Icarus it's always a good idea to be sure of one's facts!

In fact, it can be translated into something resembling English using the translator at the bottom of this page.

 « Last Edit: Jan 15th, 2005, 1:22am by ThudnBlunder » IP Logged

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Icarus
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 Re: Rubik's Cube   « Reply #40 on: Jan 15th, 2005, 7:20am » Quote Modify

Well, then, if I am translating the translation correctly, it appears that this site is merely giving instructions on solving the cube. There appears to be no particular reason to believe that this solution is anything close to minimal, so now I wonder at Net Jay's purpose in posting it? Did he totally fail to understand the point of this thread?
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"Pi goes on and on and on ...
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I wonder: Which is larger
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rmsgrey
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 Re: Rubik's Cube   « Reply #41 on: Jan 15th, 2005, 8:39am » Quote Modify

on Jan 15th, 2005, 7:20am, Icarus wrote:
 Did he totally fail to understand the point of this thread?

Since he didn't suggest that each prisoner unscrew it by 1% on their first visit, I'd say he didn't totally fail to understand the point of this thread - if nothing else, the provision of a general solution to Rubik's Cube indirectly provides an upper bound to "God's Algorithm"
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MorbidJoe
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 Re: Rubik's Cube   « Reply #42 on: Jul 24th, 2006, 2:38pm » Quote Modify

Surely the answer to 1) is 0 moves. All faces correct is a perfectley random position, just as random as any other position in fact. If I am incorrect, and the question means what is the maximum & minimum amount of moves from the same position, then the maximum is infinite.
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Icarus
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 Re: Rubik's Cube   « Reply #43 on: Jul 24th, 2006, 6:40pm » Quote Modify

No. "All faces correct" is a specifically selected position, not a random one. A random position is one in which you don't get to say what it looks like, as long as it is valid.

A better way of stating the question is "what the maximum distance of any position from solved?", where distance between positions is the minimum number of moves needed to get from one to the other.
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
dudiobugtron
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 Re: Rubik's Cube   « Reply #44 on: May 22nd, 2014, 1:36pm » Quote Modify

This has now finally been solved. (Despite the dire prediction in the 'unsolved puzzles' thread.)

Go to "cube 20 dot org" for information about the researchers and how they proved it. (Apologies, I'm not allowed to post links yet!)

The upper bound is now known to be 20.
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Hippo
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 Re: Rubik's Cube   « Reply #45 on: Mar 11th, 2016, 10:06am » Quote Modify

Oh I have missed this thread, But seems Tomas Rokicky (and co.) didn't missed the problem.

Yes there are positions requiring 20 turns in face metric.
And there is no position requiring 21. For a random position probability it requires exactly 18 turns is close to 1 (I don't remember how close, but I think its about 99% or even 99.9%).

In half turn metric there are at least 3 positions, but probably just 3 positions requiring 26 turns and no position requiring 27 turns. (I am not much sure I remember well the half turn metric results).

Now you can easily google these results.
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