Math Is Fun Forum

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

I checked for 300 dice.
E[300]/log(300) ≈ 6.12913429249

---

"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: What do you think?

Hi gAr;

It looks like it is going away from 2π.

---

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: What do you think?

Yes.
Your approximation gets closer to the actual value.

---

"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: What do you think?

It might, but I have no solid understanding as to why I should set the RHS to 1 / 2. It just seems to work. I do not know why.

---

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: What do you think?

Okay, I too do not have any idea yet.

---

"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: What do you think?

Hi gAr;

I found this pdf while looking for something else.

http://www2.truman.edu/~erickson/text3.pdf

---

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: What do you think?

Hi bobbym,

It's good, thanks!

---

"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: What do you think?

Hi gAr;

Your welcome.

They have some interesting methods of getting recurrences, generating functions for 2 variables and asymptotic forms.

---

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: What do you think?

Yes.
Didn't understand completely, but good enough to get some ideas.

---

"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: What do you think?

I am not very good with double recurrences and two variable generating functions so it is mostly past me 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: What do you think?

Okay, it's tougher than one-variable recurrences, and interesting.

---

"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: What do you think?

New Problem!

E says)
20 balling bowls are lying on a rack in a straight line.They are 3 different colors. 8 are black, 7 are blue and 5 are brown. How many ways can they be arranged so that no 2 brown balls are together? Oh, just one more thing, you must answer it using generating functions and you must show the generating function.

A says) Impossible to do it with generating functions.
B says) I do not know whether it is impossible or not but I do not have a gf either.
C says) I do not even have an answer!
D says) Hmmmm.

No one could solve it using generating functions. So they all asked E for her answer. She refused, saying that she always felt she was smarter than A,B,C and D and now she is sure.

A says) I think she is smarter than B...
B says) She might be bluffing.
C says) Yes, she is.
D says) Agreed.

Is our panel right? Or can you produce the gf?

---

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: What do you think?

Hi bobbym,

Let me consider a small example first:
2 are black, 3 are blue and 5 are brown
Is the answer 48 for this?

---

"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: What do you think?

Hi gAr;

I am getting 60 for that.

---

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: What do you think?

Hi bobbym,

Thanks.
After some refinement, one more small example:
3 are black, 3 are blue and 5 are brown
Is the answer 420?

---

"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: What do you think?

Hi gAr;

420 is correct!

---

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: What do you think?

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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi gAr;

---

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: What do you think?

Hi bobbym,

The expansion is taking too much time, so couldn't give the coefficient.

I'll try to explain.
This is how I began:
The 4 spaces between the 5 brown balls must have atleast one ball of the other 2 colors.
i) only one ball
x+y
ii) considering 2 balls
x^2 + 2xy + y^2
2xy because we can arrange black, blue or vice versa
iii) 3 balls
x^3+ 3x^2y+3xy^2+y^3

Oh, there must be a mistake in my previous post!

The other 3 spaces must contain atleast a ball, so we continue till x^8+7x^7y+...y^8,
and, hmmm, this can go only till y^7

---
It took me some time to observe that they are expansions of (x+y), since I had randomly ordered them first!

Since there are 4 spaces, we have that raised to the power 4.

The extreme ends can have 0 balls, so it starts x^0y^0,

I'll stop explaining, I'm getting a bit confused!!
But I'm sure the G.F is in that format.

edit: I saw your answer now, but anyway, do I make sense here?

Last edited by gAr (2011-06-22 03:02:08)

---

"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: What do you think?

Hi gAr;

I am sorry, but I edited my answer in post #1094. You are indeed correct.

I do not know if your reasoning is okay, but I sure would bet some dough on it. You did get the correct answer!

---

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: What do you think?

Hi bobbym,

Found the G.F, compaction applied, I can bet this is correct!!!

---

"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: What do you think?

Hi gAr;

Super! Where did you find 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: What do you think?

The reason is that we can add any number of higher coefficients, since they won't affect the lower ones!

No one could solve it using generating functions. So they all asked E for her answer. She refused, saying that she always felt she was smarter than A,B,C and D and now she is sure.

A says) I think she is smarter than B...
B says) She might be bluffing.
C says) Yes, she is.
D says) Agreed.

She'll agree now.

Thanks for this problem, a first one I'm solving with 2 variables!

Reasoning is the same as my previous post.

---

"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: What do you think?

Very good solution! Thanks for looking at the problem!

---

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: What do you think?

You're welcome!
Maybe we can generalize it to more colors?

---

"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."