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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,899

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

"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: 88,899

Hi;

*Last edited by bobbym (2013-02-16 00:35:09)*

**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.**

**Online**

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

That's an awesome formula!

I'll take a break, 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."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,899

Hi;

Okay and thanks for coming in. Have you seen Conroy's new dice problems?

**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.**

**Online**

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

Hi bobbym

These: http://www.mathisfunforum.com/viewtopic.php?id=18866?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,899

Hi;

Yes, I was telling gAr about it. We download and study those.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

Okay, I will read your discussion.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,899

Which one will you read?

**In mathematics, you don't understand things. You just get used to them.**

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

Hi bobbym,

I downloaded that, but did not go through yet.

Any problem particularly 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."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,899

There is one that is dynamite. It is mine! Look at #10.

**In mathematics, you don't understand things. You just get used to them.**

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

Hi,

Ah, yes, that looks terrific!

Did you try for a face showing up more than twice?

"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: 88,899

Yes, that is my problem. Three times a face must show.

**In mathematics, you don't understand things. You just get used to them.**

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

Solved using markov chains?

"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: 88,899

Yes, a 730 x 730 matrix. But I did not solve it, I just proposed it to him. He solved it and emailed me that he would add it to the pdf.

*Last edited by bobbym (2013-02-16 02:06:11)*

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

It reminds me of your urn problem.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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

Oh, you meant that you proposed the problem, I thought it was yours to solve!

I'll give it a try as well.

"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: 88,899

Hi gAr and anonimnystefy;

Correct!

I proposed a bigger version of the urn problem to him so that he would work on it for the pdf. Ours is just as tough but can not be phrased as a dice problem.

*Last edited by bobbym (2013-02-16 02:28:53)*

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

I think I have found a connection of that problem with this sequence.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,899

I am not following what you mean.

First, which problem?

*Last edited by bobbym (2013-02-16 03:57:12)*

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

10th problem from that pdf. The probability that the ith dice will be a third of a number is Binomial[i-1,2]/6^(i-1) *the (i-2)th number of the 6th row of the first triangles in the examples.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,899

Is it the first third of a number?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

Third?

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,899

That table is giving the probability of the the ith ball being a third one in a box. But is it the first ball to be the third one in any box or could there be others?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

The table doesn't give the probability. To get the probability you need to multiply by Binomial[i-1,2]/6^(i-1)

It is the probability that the number on the ith dice is the first one to appear 3 time.

Here lies the reader who will never open this book. He is forever dead.

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