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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,604

Yes, that is correct see post #224 for the explanation.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Howardroark****Member**- Registered: 2010-10-10
- Posts: 382

Hi gar,

Yeah i did manually.. Now i tried it with wolfram alpha

I come from a civilization which has given the world the number 0..

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

I get exactly that...

"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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,604

Okay, that is done! Now I go to the circle problem. I am half done with that. Thanks for looking at this problem guys.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi Howardroark,

Ok, I suggest you to do use maxima : http://maxima.sourceforge.net/download.html

I use sagemath, but it's not available for windows.

Maxima is good.

"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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**Howardroark****Member**- Registered: 2010-10-10
- Posts: 382

Hi gAr,

Thanks..:)

I come from a civilization which has given the world the number 0..

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

circle's problem is easier.

Hi Howardroark,

you're welcome

*Last edited by gAr (2011-02-03 23:29:07)*

"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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**Howardroark****Member**- Registered: 2010-10-10
- Posts: 382

Hi gar,

I come from a civilization which has given the world the number 0..

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,604

I use Maxima it is a great CAS!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Howardroark****Member**- Registered: 2010-10-10
- Posts: 382

Hi gAr,

Koundinya

Hi bobbym,

It was you who told me about wolfram.. Thank you.. And yeah, Geogebra too.. How do you upload images on this site?

I come from a civilization which has given the world the number 0..

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

Can we write scripts in maxima? I mostly use sage because it allows python scripts, makes the job so easy!

Hi Howardroark,

good to know you.

You can upload images using the dropdown list under "image upload"

*Last edited by gAr (2011-02-03 23:51:52)*

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,604

Have not used it in awhile ( old version ). I know it uses lisp as its programming language. Stick with Sage if you already know that.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**Howardroark****Member**- Registered: 2010-10-10
- Posts: 382

Hi gAr,

Where exactly..?

I come from a civilization which has given the world the number 0..

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**Howardroark****Member**- Registered: 2010-10-10
- Posts: 382

Hi gAR,

Sorry i saw it now.. It was too tiny.. I didn't observe it..

I come from a civilization which has given the world the number 0..

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

Ok, we can load maxima modules from sage itself. So it does everything maxima does + more. So even if recursion, z-transform etc is not available in sage, we can load maxima and solve it.

Hi Howardroark,

Glad that you found it !

*Last edited by gAr (2011-02-04 00:02:08)*

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,604

Hi;

I understand you can use it as a front end for Mathematica and Maple.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

bobbym wrote:

Hi;

4 checkers are randomly placed on a chessboard, what is the probability that no checker is in the same row or column as any other?

A) says:

B) says:

What do you like?

This is a post on first page.

(perm(8,4)^2)/perm(64,4) = 1680^2/15249024 is my answer.

When we place a checker on the board, the number of rows and columns available for the next checker decreases by 1.

So, available squares will become 7x7, 6x6 and 5x5. Hence the probability = (8*7*6*5)^2/(64*63*62*61).

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,604

Hi gAr;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

Yes, I saw rook polynomials.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,604

Hi;

That is where the 117600 comes from.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,604

A real stumper!

B throws two die. One of the die lands on an odd number, what is the probability that the two die equal 8?

A says) 2 / 9

B says) 1 / 18

C says) 2 / 27

D says) 1 / 6

What do you say?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,604

Hi gAr;

Yep! Very good! That one got me, I forgot about the nine cases that are impossible!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

Thank you!

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,604

Hi gAr;

You are very welcome. Thanks for looking at the problem.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**