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#1 2013-10-05 22:34:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,508

A stumper?

Hi;

This came up on another discussion group. Here I will show how easy this is to do with mathematica.

There are 5 different red balls, 5 different green balls, 5 different blue balls and 5 different black balls. In how many ways can they be arranged so that no two balls of same color are adjacent ?

The whole problem condenses down to this expression. ( I want to thank Robert Israel for showing me this idea.)

This produces an extremely large polynomial in 4 variables. The coefficient of

is the answer. We get it with the extremely powerful command:

Coefficient[ans, w^5 x^5 y^5 z^5]

the answer is 134631576.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#2 2013-10-06 00:19:58

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,820

Re: A stumper?

How does it work?


“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

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#3 2013-10-06 00:23:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,508

Re: A stumper?

It looks like it is the matrix version of a gf. How it works, I never did figure out, but I can use it.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#4 2014-03-17 23:56:29

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: A stumper?

Hi,

I think I got a hang of doing things in J.

Here's a simulation for an approximate answer:

sim=: 3 : '0=+/+/(2 4 8 16)=/2+/\(20?20){5#1 2 4 8'
((!20)%(!5)^4)*(+/%#)(sim "0) 1000000#0

= 135712661.692608


"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 2014-03-18 02:51:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,508

Re: A stumper?

Hi gAr;

That is close!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#6 2014-03-18 03:09:49

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: A stumper?

Hi,

Yes!
Is there any command in Mm to get moving averages?


"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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#7 2014-03-18 03:22:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,508

Re: A stumper?

M, is bloated to the extreme. There is command for everything. Whenever I do not find a command that does exactly what I want I always think I did not look in the right place!

Try MovingAverage in the help.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#8 2014-03-18 04:08:09

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: A stumper?

Ah, yes!
I should have searched before asking!


"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."

Offline

#9 2014-03-18 04:09:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,508

Re: A stumper?

Hi;

No problem. Glad to help.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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