Math Is Fun Forum

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

Looks like he has misunderstood the question or the question is different there!
Isn't it mentioned that there must be 2 balls in each box?

Is it the same question in that forum too?

---

"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 do not agree with his answer either. I have thanked him because he is a volunteer and I respect what he is doing. I make mistakes too, plenty of them so I am going to just let it go.

That does not take away from what you have done and it is time to say good job!

On the other forum the balls are labeled a1,a2,b1,b2,c1,c2,d1,d2. The rooms are labelled like our problem. I do not think they are even close to an 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?

Yes, it's okay. We believe our ways.

But what I wanted to know is whether it's mentioned there that there should be exactly 2 balls in each box.

---

"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?

Yes, 2 balls in every box. I explained that to him and the other forum has the same problem. Except the balls are numbered.

---

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.

---

"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:

Express 

in the best symbolic form.

A says) Impossible.
B says) Easy!
C says) 8.888783 x 10^6 296 512
D says) Yep!
E says) You guys should see what B did. It is much cleaner than that floating point answer.

What do you get?

---

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,

Last edited by gAr (2011-05-15 04:15:53)

---

"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,

Ah, yes, a small typo!

---

"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;

No problem! Good 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?

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?

Your welcome!

New problem;

A and B never quit. They both decide to run for town mayor. Now A believes with his excellent education that he is smarter than B whose education consisted of 50% attendance at Whats A Matter U. He believes he will win.

They tally the votes and A wins 381 to 254.

B says) Good win A, I thought I might win when the election was tied but you pulled away.
A says) I do not ever remember the count being tied. I think you are exaggerating. Besides with such an overwhelming win ties are very unlikely.
B says) I do not agree. Counting the votes one at a time like they did, ties are very likely. I would estimate there is a 79% chance of a tie score occurring during the counting.
A says) Rubbish! Chance of a tie is only about 10%.
C says) 50%, either it is tied or it isn't. So that is 1 to 1.
D says) I agree with B but it is more like 83%

Can you estimate the chance that a tie occurred? That would mean one or more.

---

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?

Hmmm, and I wonder how!

*edit: When I calculate your fraction, I get : 0.2006319115323854660347...

Last edited by gAr (2011-05-16 04:08:27)

---

"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 did not get it either. I researched on Ballot problems and found one book that poses this exact problem in different words. Give me a little time and I will post what I do know about 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?

Hi bobbym,

Okay.

I'm fairly sure that formula is right.

Suppose the votes are 3 A's and 2 B's:

The favorable outcomes are:
ababa, abaab. abbaa, aabba,
baaba, baaab, babaa, bbaaa
which is also the number obtained from the formula.

And the value I get from your fraction is closer to 0.2

---

"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: What do you think?

I think I have missed some sequences, I'll try the problem again.

---

"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,

Yes, I too found some references.

http://en.wikipedia.org/wiki/Bertrand%27s_ballot_theorem

http://books.google.co.in/books?id=QiuqPejnweEC&pg=PA38&lpg=PA38&dq=ballot+tie+problem&source=bl&ots=uJ1vTx2weq&sig=IZ_7RLIztbVc4VD2hcA6VPpA7ms&hl=en&ei=BVDRTeiEB4rYrQfipsjCCg&sa=X&oi=book_result&ct=result&resnum=2&ved=0CB8Q6AEwAQ#v=onepage&q=ballot%20tie%20problem&f=false

Thanks for the problem, good one!

---

"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 is a variation of the random walk. It is in the Mosteller and Feller books. Thanks for the links.

---

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 thought of random walk, but couldn't get further.

---

"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!

Inspired by the fact that it is difficult to count a block walk when there are restricted vertices see this:

http://www.mathisfunforum.com/viewtopic … 96#p162496

Post #175 and on.

E devises the following problem. Picture a grid of streets. You are standing at the lower left. It is marked ( 1, 1 ) you must get to ( 500, 501 ) the upper right. Paths through ( 18 , 18 ) are prohibited. How many paths are there?

A says) Impossible, we can think of this as a morphism of all the graphs that do not exist.

B says) I solved it for the general ( n , n ).

C says) I ran a program, there are 12345678910111213141516171819202122 ways which is a Champernowne's number.

D says) There are

E says) I am laughing too hard but B has a general solution.

Extra credit:

After finding the number of paths can you generalize like B did?

---

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;

I am putting my work together on this problem. I will be able to check your answer as soon as I can.

---

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.