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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

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: 86,481

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

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

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: 86,481

Re: A stumper?

Hi gAr;

That is close!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

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

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: 86,481

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

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

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."

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: A stumper?

Hi;

No problem. Glad to help.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

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