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

Hi bobbym,

I'm beginning with markov chains, looks very interesting!

I started with this short introduction: http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter11.pdf

I got the idea from your way to obtain 34. I need to check more related problems.

"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: 105,295

Hi gAr;

Thanks for the link. They are a very powerful tool.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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

Hi bobbym,

Yes, I recognize it. What I studied before just scratched the surface.

I'm going through R-project, looks nice to help us with simulations.

*Last edited by gAr (2011-02-25 19:42:52)*

"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: 105,295

Hi gAr;

Sometimes simulations are all you have to answer 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.****No great discovery was ever made without a bold guess. **

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

Hi bobbym,

A cryptogram:

LD GZH QFC'O UV BLCS OEVC FO AVFTO UV RFKHV.

A says) cryptograms give me a headache.

B says) I got it. It was easy.

C says) I used a computer, then it was easy.

D says) Takes 5 minutes.

I guess:

*Last edited by gAr (2011-03-02 01:23:54)*

"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: 105,295

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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

Oh, yes. I made a mistake. But I wasn't sure whether "kind" would fit in.

"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: 105,295

That is okay. You did well. I am satisfied. That one has been there a while. Thanks for looking at it.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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

Hi,

Thank you!

5 die are thrown at once. What are the odds that just 2 die are the same?

a says) I ran a program and the answer is: 3600 / 7776

b says) You don't need a computer the GF is ( a + b + c + d + e + f )^5, just expand that and you are done. By the way it is 3600 / 7776

c says) I used the binomial distribution and got 25 / 216

d says) I did it like this:e says) a and b are right but no one can expand that expression without a computer.

f says) Takes less than 5 minutes to expand b's expression, but it is wrong anyway 144 / 216 is right.

Can you show me the generating function please, I find it interesting.

*Last edited by gAr (2011-03-02 01:55:27)*

"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: 105,295

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.****No great discovery was ever made without a bold guess. **

**Online**

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

Oh, good.

And yes, doesn't appear very neat !

Thanks for showing the method.

"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: 105,295

Sometimes a GF as well as solving the problem can help suggest a method. By looking at them it is now possible to come up with a better way.

Each a^2 to f^2 will have a coefficient of 60.

Once you picked a square there are 5 choose 3 ways to pick the other letters. Also there are 6 different squares to choose from.

6 * 10 * 60 = 3600

When you choose different letters it is easier to compute the coefficients. When you have a single variable GF it is harder because the powers of x get added together.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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

Hi bobbym,

If r1, r2 and r3 are the roots of

and a ≠ 0 and

find a.

A says) No solutions.

B says) There are many answers for a but only one integer answer.

C says) There is only one answer for a.

D says) There are many answers but none of them are integers.

Who is right?

After finding the roots and substituting in the condition:

How to tackle this monster? I guess that there are no real or integer roots for a.

Program goes out of memory and crashes!

"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: 105,295

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.****No great discovery was ever made without a bold guess. **

**Online**

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

Hi bobbym,

Ok, got it.

Now I remember!

"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: 105,295

Glad to help!

New problem:

A only has 50 dollars. He wants to win a small lottery. There are 50 lotteries in town. Each one sells 1000 tickets at 1 dollar apiece. He wonders about how he can best maximize his chances of winning one. He buys 1 ticket in each lottery and is happy. B says that was not the best idea. Putting all 50 into one lottery was smarter. C says what nonsense, the chances are the same. D says I have heard B's argument and it is gibberish.

B says just listen for a second. Supposing there were 10 lotteries with 10 tickets in each and you had 10 dollars. If you buy every ticket in one lottery you are sure of winning it. If you spread it around like A did you will probably come up empty. Increasing the number of lotteries and tickets will diminish my idea but it will always be better than A's idea.

What do you think of B's arguments and A's gambling skills?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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

Hi bobbym,

*Last edited by gAr (2011-03-02 21:45:23)*

"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: 105,295

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.****No great discovery was ever made without a bold guess. **

**Online**

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

Hi,

How many integers from the set:

{5000, 5001, 5002, 5003, 5004, 5005, ... 10000}

are there that when you some the digits you get a sum of 21.

A says 123;

B says none

C says (10000 - 5000 -2) / 21

"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: 105,295

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.****No great discovery was ever made without a bold guess. **

**Online**

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

Hi bobbym,

Thank you. I thought I can do something with combinations with repetition. But it became surprisingly difficult.

Discussing the sum:

A says that n is divisible by 12347, B says n isn't divisible by 12347. Who is right?

*Last edited by gAr (2011-03-03 01:20:48)*

"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: 105,295

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.****No great discovery was ever made without a bold guess. **

**Online**

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

Hi,

Easy one:

http://images.zaazu.com/img/sleep-anim- … medium.gif

How many integers don't have a zero and sum to at most 8?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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

Hi,

Another question's answer:

B says "hey I found a neat proof that a square is the rectangle with the biggest area for a fixed perimeter. and it doesn't use any calculus. Instead it uses a little error analysis borrowed from numerical analysis.

If the rectangle is a square then the area is s*s = s^2, If it is a rectangle then it can represented as s + e and s - e. Sort of like a 5x5 square and a 7x3 rectangle, e would be 2 in that case. The area of that rectangle is (s + e)(s - e) = s^2 - e^2. Clearly s^2 is greater than s^2 - e^2, so we are done.

A says) Nonsense! If that is a proof I am Eisenstein!

B says) Sure it is a proof!

C says) Who is Eisenstein?

D says) I haven't disagreed with A since 1971 and I ain't starting now!

E says) Another crazy idea from B!Who is right?

"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: 105,295

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.****No great discovery was ever made without a bold guess. **

**Online**