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

Hi bobbym,

Thank you!

"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: 89,124

Hi gAr;

Not too difficult but cute problem.

**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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,124

Hi hammana;

**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

Hi,

Yes, it's a good 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."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,124

Hi;

Glad you and anonimnystefy had some fun with it.

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

Hi bobbym

It's a nice problem, and the first one of yours I solved successfully!

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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**hammana****Member**- Registered: 2012-03-02
- Posts: 48

The average value calculated from the table (post 125) is 3.76

We could also say that the number of white marbles is multiplied by .75 at each operation so the final result is :

50*(0.75)^9 =3.7541, This method does not seem very rigorous, but the result is practically identical to the simulation result.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

Hi bobbym

For #1 I got an explicit formula

Is it correct?

*Last edited by anonimnystefy (2012-03-06 08:38:33)*

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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**hammana****Member**- Registered: 2012-03-02
- Posts: 48

Results given in post 125 are wrong because i assumed that the replacement operation was carried 9 times. A new simulation assuming the replacement carried 10 times gives an aveerage of 2.812 and 50*(0.75)^10=2.8157

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,124

Hi anonimnystefy;

Yes that is correct! Very good.

Hi hammana;

Very good answer! Well done.

**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: 15,609

Hi bobbym

I did it using the magnificent GF's.

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: 89,124

Well let me see.

**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: 15,609

Are you really gonna make we swype all that? I'm probably not gonna be able to use my laptop or my desktop till thursday evening.

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: 89,124

Then Thursday evening you will do it.

**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: 15,609

Sure! Can I expect more problems soon.

And you were right, these ones are easier.

*Last edited by anonimnystefy (2012-03-07 10:15:40)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,124

As soon as I find one. I can not guarantee they will all be easy.

**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: 15,609

I wonder if it will be before or after thursday night.And they do not have to be easy, just not to be very hard.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,124

I am waiting for your generating function...

**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: 15,609

Hi bobbym

It's probably gonna be on thursday afternoon after all.I am finishing with studying tomorrow and then I'm a free man for the next week.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,124

But this is only Wednesday. Why are you free for a week?

**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: 15,609

From the thursday evening to the sunday evening of the next week I'm free.on sunday I have a physics competition so I'm not going to school on friday, and the next week I'm off because I have a national mathematics competition.

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: 89,124

Who will you compete against?

**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: 15,609

Against other grade 10 students from the while Serbia that passed the regionals.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,124

How have you prepared?

**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: 15,609

I have but I have till the next week's Friday to prepare as much as I can.

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