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#26 2013-12-30 04:53:52

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
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Re: Simple Combinatorics Problem


and then we collect the coefficient of x^20.

A post was deleted or I was daydreaming?


'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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#27 2013-12-30 04:55:55

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Simple Combinatorics Problem

Very, very good! How did you know that?


Two posts were deleted because I do not want to jump ahead with probability gf's just yet.

Now please compute the answer.


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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#28 2013-12-30 04:58:29

Agnishom
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From: Riemann Sphere
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Posts: 24,974
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Re: Simple Combinatorics Problem

Looks like it is 35. How do I grep coefficients in Maxima? By the way, what does grepping mean?


'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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#29 2013-12-30 05:01:00

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Simple Combinatorics Problem

Grep is a command line utility for searching going back to Windows 98. Grepping must mean picking them out.


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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#30 2013-12-30 05:03:33

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
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Re: Simple Combinatorics Problem

Is it a standard english word? How do I grep Coefficients in Maxima? Is 35 correct?


'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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#31 2013-12-30 05:06:01

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Simple Combinatorics Problem

Grepping is a technical term. 35 is correct and there should be a coefficient command in Maxima to do the job. But even if you can not find it we will not be doing ones that you can not just expand out.


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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#32 2013-12-30 05:09:22

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
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Re: Simple Combinatorics Problem

But even if you can not find it we will not be doing ones that you can not just expand out.

What does it mean?


'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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#33 2013-12-30 05:11:49

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Simple Combinatorics Problem

What does what mean? Grepping or the quote?


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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#34 2013-12-30 05:15:21

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
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Re: Simple Combinatorics Problem

Never mind; I've found the command


'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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#35 2013-12-30 05:19:01

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Simple Combinatorics Problem

Very good! I found it too.

How did you know to raise it up to the 4th power?


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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#36 2013-12-30 05:21:48

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
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Re: Simple Combinatorics Problem

Ofcourse I cannot raise a sixterm polynomial to its 4th power by hand.

(%i12) coeff((expand((x + x^2 + x^3 + x^4 + x^5 + x^6)^4)),x,20);
(%o12)                                35

'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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#37 2013-12-30 05:24:01

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Simple Combinatorics Problem

Are you now ready to try your hand at a real combinatorics problem? One that would start to stump even the best NCR getters.


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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#38 2013-12-30 05:25:09

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
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Re: Simple Combinatorics Problem

Yes; ...


'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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#39 2013-12-30 05:29:04

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Simple Combinatorics Problem

A mother wishes to share 20 dollars between Sally ,Edna, and
son Jack, so that they each receive at least $5, and nobody receives more than $10, and Edna gets an even amount. How many ways are there of doing this?


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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#40 2013-12-30 05:37:22

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
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Re: Simple Combinatorics Problem

(x^5 + x^6 + x^7 + x^8 + x^9 + x^10)*(y^5 + y^6 + y^7 + y^8 + y^9 + y^10)*(z^5 + z^6 + z^7 + z^8 + z^9 + z^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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#41 2013-12-30 05:38:46

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Simple Combinatorics Problem

We do not need three different variables. I only did that for illustration purposes earlier.


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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#42 2013-12-30 05:47:19

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
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Re: Simple Combinatorics Problem

If you do not need three different variables, then how can you ensure the fact about the even amount?

(%i18) coeff((expand(((x^5 + x^6 + x^7 + x^8 + x^9 + x^10)^2) * (x^6 + x^8 + x^10))),x,20);
(%o18)                                 9

xu drani

Last edited by Agnishom (2013-12-30 05:48:20)


'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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#43 2013-12-30 05:50:15

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Simple Combinatorics Problem

Excellent work! That is correct.

Supposing you were trying to convince me that gf's were better. Supposing you believed that, sum up in your own words why generating functions are easier.


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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#44 2013-12-30 05:52:55

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

Re: Simple Combinatorics Problem

Supposing you were trying to convince me that gf's were better. Supposing you believed that, sum up in your own words why generating functions are easier.

They are easier if you have a computer with you.


'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

#45 2013-12-30 05:56:46

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

Re: Simple Combinatorics Problem

I still do not understand how you gAr got the gf for the original problem


'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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#46 2013-12-30 05:57:19

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Simple Combinatorics Problem

That is only the tip of the iceberg. Is

easy to do by hand?

Big problems usually generate big numbers, no matter what method you use you will need a computer. The real thing is that the gf approach reduces each problem to mere multiplication of polynomials! Once you formulate it and you see how easy that is even for a tough problem then you only have to multiply.


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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#47 2013-12-30 05:59:39

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

Re: Simple Combinatorics Problem

Agnishom wrote:

I still do not understand how you gAr got the gf for the original problem


'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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#48 2013-12-30 06:04:24

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Simple Combinatorics Problem

Do you understand this one?

Remember I said I only used the 3 variables for illustration. Well gAr, combined o and y into one variable.

And by the way, many of these can be expanded by the binomial theorem without a computer but not as quickly.


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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#49 2013-12-30 06:11:26

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

Re: Simple Combinatorics Problem

I do not understand why there is a 1 +


'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

#50 2013-12-30 06:15:27

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Simple Combinatorics Problem

(1 + o) means you can choose zero or one o.


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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