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

Hi bobbym,

I couldn't solve this without a computer.

"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: 105,731

Hi gAr;

That is okay. I remember you asked me about a similar problem. I think it was mississippi. When I came across this one I stumbled on a solution of sorts. I figured you would like to work on it first so I posted here as a question.

_________________

**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 bobbym,

Thanks for the solution. I couldn't find all the the possibilities and was stuck.

I was thinking whether there's a formula for any number of letters and repetitions.

The question I asked was: http://www.mathisfunforum.com/viewtopic.php?id=14910

"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: 105,731

Hi gAr;

I am checking a recurrence right now.

**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 bobbym,

Ok.

All the best with that.

"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: 105,731

Hi gAr;

This is the post where you asked me a similar question:

http://www.mathisfunforum.com/viewtopic … 97#p166997

Post #11

**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, Ok. I forgot about it! Your memory is good.

"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: 105,731

I just remembered that I could not do it either. It has been bothering me since then. I found it in the Tucker book and he did not solve it twice because it was even and then he moved it in later editions.

**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

Oh, I see.

Is this related to pattern avoidance problem?

"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: 105,731

Hi gAr;

I do not know but I am thinking about relating it to a lattice structure. Here is the recursion I am working on. A guy named Makar gave it to me after he saw my answer.

f(p,q,r) = f(p,q-1,r-1) + f(p-1,q,r-1) + f(p-1,q-1,r) + 2 f(p-1,q-1,r-1)

**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 bobbym,

Ok.

What are p,q,r? The three letters?

"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: 105,731

Hi gAr;

The number of each letter. For instance f(2,3,4) is a,a, b,b,b, c,c,c,c.

**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

Okay, I'll check.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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

Works for all values I tried! Do you know how he derived it?

"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: 105,731

Hi gAr;

I have not figured that out yet. I think it is the same type of reasoning as when you do an expectation using the formula.

I am going to take about a half hour break, see you in a bit.

**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 bobbym,

Ok.

"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: 105,731

Hi gAr;

What values have you tried it on?

**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 bobbym,

I tried the following values:

(p,q,r) :

(2,1,1)

(2,2,1)

(2,2,2)

(3,2,2)

(3,3,2)

(3,3,3)

(4,3,3)

(4,4,3)

(4,4,4)

"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: 105,731

Hi gAr;

Okay, that looks pretty good then. It appears to be right.

**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

I haven't seen many examples of recursion with more than one parameter. So cannot think about the derivation for this kind!

Okay, I'll be away for few minutes, see you later.

"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: 105,731

Okay. it is harder than with one variable but there is a 2D block walk example that would help explain 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 bobbym,

That's ok.

Thanks for showing the recurrence formula.

"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: 105,731

Hi gAr;

Your welcome. Thanks for checking some values.

**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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,731

Hi;

New Problem!

Can you find any solution of:

with a,b,c,d all positive and different.

A says) Yes, I can and without a computer.

B says) Yes, that is right and I did it too.

C says) Well, well, well, both A and B agreeing and both wrong!

D says) Yes, that is a first. You are right C there are no solutions.

Can you find an answer? Can you find A or B's idea for full credit?

**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 bobbym,

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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