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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

You were there when I answered John Franklin's question. It was so easy he picked up on it right away. Do you need more than that?

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

Ok, I get that one, but look at this problem;

You have ten pigeons and you have to arrange them into three cages so that in every cage the is at least 1 pigeon.You can assume the pigeons to be all the same.the same goes for the cages.In how many ways can you arrange the pigeons into cages under the given conditions?

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

Hi;

There are 36 ways.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

How did you get that?

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

You are trying to solve the diophantine equation

a+b+c=10 with 0<a,b,c<11

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

That's pretty much it.But how do you arrive at the answer with GF's?

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

Now check the coefficient of x^10.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

But what about the condition that there of at least one pigeon on each cage?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

Hi;

Took a while to edit post #82. The polynomial takes that into account automatically.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

So we just take out the 1.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

Yes. The 1 represents x^0. There is no 0 choice because there must be at least one pigeon per box.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

Hi bobbym

Then I'm clear on that part.Just have one question.For the x^10 we use asymptotic analysis on the forum right? But, when I do these problems when I'm not allowed to use Wolfram and that stuff, how do I then get the Laurent series?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

You do not need a Laurent series here. There are ways that help you get the coefficients we need. But they are rather limited. There are limits to what can be done by hand.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

And what's that way? And what if I wanted the answer in binomial form?

Btw, do you know what Eurovision is?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

Hi;

The other method would be to use series methods on

it does not look very promising though.

I have not heard of Eurovision.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

Ok, but if I wanted it in the binomial form?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

Then you would have to solve the diophantine equation using the formula.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

But is there a way to get it directly out of the GF?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

In this case you could play spot the pattern with the generating function. Other methods do not look promising.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

Ok, then.When can we expect more problems?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

As soon as I get back here.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

Back where?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

Back in the forum. I have some work to do.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

So where's the problem?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,998

**Baffler #2**

**A ship is sailing on a course from the origin. It follows the path y= 3.14 x. It has a speed of 1 / 3 units per second. A submarine is located at (5,0). The sub knows the ship is oblivious to its existence. The sub would like to torpedo the warship. Torpedoes travel at 1 / 2 units per second and travel in straight lines. The sub commander's hobby is mathematics. He fires and sinks the ship! What is the equation of the torpedoes flight?**

**A says) Too easy, here is the answer!**

**B says) I am astounded, you got the right answer!**

**C says) A is my hero.**

**D says) Hip hip hooray!**

**E says) Even a blind squirrel finds an acorn now and then.**

**B says) How true.**

**Find that equation. If A got it then so should you!**

**In mathematics, you don't understand things. You just get used to them.**

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