Math Is Fun Forum

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Hi bobbym,

I couldn't solve this without a computer.

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"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

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

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Oh, I see.
Is this related to pattern avoidance problem?

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Hi bobbym,

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

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Okay, I'll check.

---

"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."

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

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

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Hi bobbym,

Ok.

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

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)

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

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.

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Hi bobbym,

That's ok.
Thanks for showing the recurrence formula.

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Hi bobbym,

---

"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."