Math Is Fun Forum
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#1 2014-05-22 18:34:27
Combinatorica
In how many ways can I create a string of length 10 consisting only of A, B and C such that it does not contain the substring 'AB' and 'BA'?
'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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#2 2014-05-22 20:36:08
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Combinatorica
Hi;
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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#3 2014-05-22 20:49:41
- ElainaVW
- Member
- Registered: 2013-04-29
- Posts: 580
Re: Combinatorica
Hello Agnishom:
Last edited by ElainaVW (2014-05-22 20:53:43)
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#4 2014-05-23 04:40:50
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Combinatorica
Last edited by gAr (2014-05-23 05:03:03)
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#5 2014-05-23 13:52:41
Re: Combinatorica
Hi gAr;
please explain a bit more. i do not understand anything...
Bobbym, EVW: I've already brute forced it with a computer and found it to be 8119
'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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#6 2014-05-23 14:43:09
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Combinatorica
I do not know what she did but I did not brute force it. Experimental math does not mean brute force.
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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#7 2014-05-23 16:11:37
Re: Combinatorica
What did you do? I bruted it
'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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#8 2014-05-23 17:00:34
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Combinatorica
Hi,
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#9 2014-05-23 17:05:20
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Combinatorica
What did you do? I bruted it
Hmmm, yes I know.
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 2014-05-23 20:09:34
- ElainaVW
- Member
- Registered: 2013-04-29
- Posts: 580
Re: Combinatorica
Bobbym, EVW: I've already brute forced it with a computer and found it to be 8119
Hohummm. 
stripping the labels.
Answer is the first row. The generating function is now easy
Even though this is very nice there are some advantages to the brute force solution. Do you know why?
Last edited by ElainaVW (2014-05-23 20:10:48)
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#11 2014-05-23 20:15:17
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Combinatorica
I used that idea, because gAr showed me that. Why the brute force way has some advantages? There are two reasons really.
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 2014-05-23 21:50:34
Re: Combinatorica
Please explain post 10
'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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#13 2014-05-23 22:02:24
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Combinatorica
It is called and incidence matrix and it counts the number of paths from one vertex to another in 10 stages or steps.
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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