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#1 2014-07-22 01:24:16
- rom1
- Guest
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
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'
I'm not crazy, my mother had me tested.
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#3 2014-07-22 01:56:36
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Number of movements for Rubik's cube identity algorithm
There isn't such an algorithm.
Consider the corners of the cube:
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
The knowledge of some things as a function of age is a delta function.
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#4 2014-07-22 02:16:31
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'
I'm not crazy, my mother had me tested.
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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!
What is your favorite color?
It's a bluish-yellow
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#6 2014-07-22 02:57:45
- ShivamS
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- Registered: 2011-02-07
- Posts: 3,648
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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#8 2014-07-22 03:06:59
- ShivamS
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- Registered: 2011-02-07
- Posts: 3,648
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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#10 2014-07-22 04:07:30
Re: Number of movements for Rubik's cube identity algorithm
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'
I'm not crazy, my mother had me tested.
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#11 2014-07-22 04:44:39
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#12 2014-07-22 05:13:37
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Number of movements for Rubik's cube identity algorithm
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
The knowledge of some things as a function of age is a delta function.
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#13 2014-07-22 05:46:15
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Number of movements for Rubik's cube identity algorithm
The Geebra can do it.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#14 2014-07-22 06:16:33
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
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
The knowledge of some things as a function of age is a delta function.
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#15 2014-07-22 06:29:18
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#16 2014-07-22 07:15:25
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
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
The knowledge of some things as a function of age is a delta function.
Offline
#17 2014-07-22 07:53:38
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#18 2014-07-22 08:04:14
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
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
The knowledge of some things as a function of age is a delta function.
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#19 2014-07-22 08:13:36
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
#20 2014-07-22 08:35:47
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
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
The knowledge of some things as a function of age is a delta function.
Offline
#21 2014-07-22 08:46:54
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
#22 2014-07-23 01:24:30
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'
I'm not crazy, my mother had me tested.
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#23 2014-07-23 01:28:26
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#24 2014-07-23 02:40:49
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'
I'm not crazy, my mother had me tested.
Offline
#25 2014-07-23 04:11:53
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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