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#1 2014-07-22 01:24:16

rom1
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Number of movements for Rubik's cube identity algorithm

Hello everybody,

A collegue of mine asked me an interesting question : is there any identity algorithm for the Rubik's cube (an algorithm that does not change the cube) that is composed of an odd number of movements ?

I call a movement any quarter of turn (L, L', R, R', U, U', D, D', F, F' B, B').

I have some identity algorithm examples :
RR' -> 2 moves
R2 R2 = RR RR -> 4 moves
(R2U)*30 -> 90 moves
(RU')*63 -> 126 moves
(RU)*105 -> 210 moves

#2 2014-07-22 01:41:31

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 17,172
Website

Re: Number of movements for Rubik's cube identity algorithm

I do not think so, but it will be fun trying to prove that. Thanks for sharing the problem.

What is your favorite color?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#3 2014-07-22 01:56:36

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Number of movements for Rubik's cube identity algorithm

There isn't such an algorithm.

Consider the corners of the cube:
cube.png

After each move, some of the odd labeled corners go into places of even labeled corners and vice versa. So, after any odd number of moves, odd corners end up in even numbered places and the even corners end up in odd numbered places, so such an algorithm is not possible.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#4 2014-07-22 02:16:31

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 17,172
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Re: Number of movements for Rubik's cube identity algorithm

Brilliant!

Now, what did you use to draw that cube?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#5 2014-07-22 02:56:00

rom1
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Registered: 2014-07-22
Posts: 1

Re: Number of movements for Rubik's cube identity algorithm

Ok, simple and efficient, thank you anonimnystefy!

Agnishom wrote:

What is your favorite color?

It's a bluish-yellow

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#6 2014-07-22 02:57:45

ShivamS
Member
Registered: 2011-02-07
Posts: 3,555

Re: Number of movements for Rubik's cube identity algorithm

That is an impossible color.

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#7 2014-07-22 03:00:47

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: Number of movements for Rubik's cube identity algorithm

I think they call it green.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#8 2014-07-22 03:06:59

ShivamS
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Registered: 2011-02-07
Posts: 3,555

Re: Number of movements for Rubik's cube identity algorithm

Not blue and yellow in equal proportions.

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#9 2014-07-22 03:15:46

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: Number of movements for Rubik's cube identity algorithm

I never thought about mixing it in equal proportions.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#10 2014-07-22 04:07:30

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 17,172
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Re: Number of movements for Rubik's cube identity algorithm

ShivamS wrote:

Not blue and yellow in equal proportions.

In what proportions then?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#11 2014-07-22 04:44:39

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: Number of movements for Rubik's cube identity algorithm

I used to mix a can of blue with a can of yellow and always got 2 cans of green.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#12 2014-07-22 05:13:37

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Number of movements for Rubik's cube identity algorithm

Agnishom wrote:

Brilliant!

Now, what did you use to draw that cube?

Found it on the interwebs.

Last edited by anonimnystefy (2014-07-22 05:14:10)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#13 2014-07-22 05:46:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: Number of movements for Rubik's cube identity algorithm

The Geebra can do it.


fjUrLC6.gif


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#14 2014-07-22 06:16:33

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Number of movements for Rubik's cube identity algorithm

Yeah, but it was easier to just find a pic on the interblag than to make it in GG or anywhere and upload it on imgur.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#15 2014-07-22 06:29:18

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: Number of movements for Rubik's cube identity algorithm

I know, I was talking to Agnishom.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#16 2014-07-22 07:15:25

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Number of movements for Rubik's cube identity algorithm

Ah, yes, sorry.

Unrelated to the topic, have you gotten around to looking at Elaina's problems yet?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#17 2014-07-22 07:53:38

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: Number of movements for Rubik's cube identity algorithm

Hi;

No I have not and she is back in Florida for 3 weeks so I will not have to. I am currently very busy with Ubuntu.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#18 2014-07-22 08:04:14

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Number of movements for Rubik's cube identity algorithm

What about Ubuntu?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#19 2014-07-22 08:13:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: Number of movements for Rubik's cube identity algorithm

I am switching over to it and any such move is very difficult. I am almost done but almost is not good enough.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#20 2014-07-22 08:35:47

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Number of movements for Rubik's cube identity algorithm

Having any problems?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#21 2014-07-22 08:46:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: Number of movements for Rubik's cube identity algorithm

Multitudes of them. I have an XP mentality and it does not fit in a linux world.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#22 2014-07-23 01:24:30

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,172
Website

Re: Number of movements for Rubik's cube identity algorithm

You will have a linux mentality soon. What problems do you have?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#23 2014-07-23 01:28:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: Number of movements for Rubik's cube identity algorithm

I am looking for a application dependent fw. There are many for windows but none it seems for linux.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#24 2014-07-23 02:40:49

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,172
Website

Re: Number of movements for Rubik's cube identity algorithm

Why not ask on askubuntu.com?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#25 2014-07-23 04:11:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: Number of movements for Rubik's cube identity algorithm

That is where I was looking as well as a lot of other places.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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