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#1 2014-05-22 18:34:27

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
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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

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

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. sad

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

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.

Offline

#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.

Offline

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