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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,273

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.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,016

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

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,273

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.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,273

Hi gAr;

That is close!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,273

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.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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

Ah, yes!

I should have searched before asking!

"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: 105,273

Hi;

No problem. Glad to help.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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