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**cooljackiec****Member**- Registered: 2012-12-13
- Posts: 162

In how many ways can we distribute 13 pieces of identical candy to 5 kids, if the two youngest kids are twins and insist on receiving an equal number of pieces?

I see you have graph paper.

You must be plotting something

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

I would say 308.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,599

Hi;

**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: 15,657

From bobbym's Diophantine equation in the post above we can form the GF:

*Last edited by anonimnystefy (2013-01-08 05:08:17)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Hmmm, but do ye have the diophantine equation?

**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: 15,657

Hi bobbym

I was still editing when you posted. See the post again.

*Last edited by anonimnystefy (2013-01-07 12:59:49)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Hi;

So where is the diophantine equation?

Oh sorry, you peeked and I did not see.

**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
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I am refering to your diophantine in the post just above.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Yes, I see that.

How about the recurrence:

with a(0)=1,a(1)=3

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**anonimnystefy****Real Member**- From: The Foundation
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I think that I can even get a closed form for the terms...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Hi;

That may be a little bit more difficult than it appears for the same reason why that recurrence is false!

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Got it!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Hi;

You did not read post #11, that is not quite correct.

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**anonimnystefy****Real Member**- From: The Foundation
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I did read it, but I do not see what is wrong...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Supposing I asked you to use that formula for 50 pieces of candy would you get the right answer?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I am getting 12051.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Yes, that is correct.

I meant coming up with an analytical form for the coeffs of the expansion of the polynomial in post #3. But I guess that is not really that important.

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**anonimnystefy****Real Member**- From: The Foundation
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So my formula in post #9 is correct?

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**bobbym****Administrator**- From: Bumpkinland
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Hi;

Yes, I believe it is. I got,

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**anonimnystefy****Real Member**- From: The Foundation
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I think the two are same... I just put mine in the form above because of the common expression 1+(-1)^n. It is noce to know that that part is 0 when n is odd.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Hi;

I know how I got mine, may I ask how you got yours?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Partial fractions, then expanding.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Hi;

Did them by maxima?

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**anonimnystefy****Real Member**- From: The Foundation
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Partial fractions in Maxima and expanding by hand.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Hi;

Okay, somehow though I do not think these answers are what the OP will require.

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