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

Hi,

You're welcome.

"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: 86,730

Hi gAr;

Have you seen juans last problem?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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

Which one, finding miinimum 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."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,730

Hi;

Sorry, did not see he posted some after that. Take a look at this one. I solved it but in an unconvincing way.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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

Okay, I'll see that and post there if I have anything to say...

"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: 86,730

Thanks, that would be good. My answer is in post #33 of that thread.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,730

**New Problem:**

**A and C are asked at their new job to tackle a problem. The casino would like to know what the expected difference is of the total of the first and the total of the second die if a pair are thrown 123456787654321 times. For example if a pair are thrown 3 times (3,6), (5,4), (1,1) the sum of the first die is 3+5+1=9 and the sum of the second die is 6+4+1=11 the difference is 2.**

**A instructs C to run a simulation assuring him that no mathematical solution is possible. He claims that his vast knowledge of meromorphic functions proves this. C believes him and runs a large simulation that takes 3 days of computer time.**

**The supervisor of the computing division is outraged at the 3 days usage and asks C for an explanation. C explains that he was correct and A agrees. The supervisor immediately fires A and C.**

**A and C immediately run back to B complaining about the supervisors treatment. B starts to laugh at their misfortune,**

**B says) You two turkeys really are overcooked. Of course there was a simple mathematical solution. You wasted 3 days on a giant mainframe and should be fired.**

**A says) Hold on B, I have had enough of your insolence. My mathematical knowledge dwarfs yours and that supervisor's too. I am right and we were fired unjustly.**

**D says) Here, here! A you are truly a champion of justice and mathematics too.**

**E says)A is a dullard and C is even worse for believing him!**

**Is A being fired cool with you? Is B right that they wasted the casino's money?**

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

Hi bobbym

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

bobbym wrote:

This prob came up somewhere else:

A coin with probability p of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is {2,4,6,8,10...} is 2/5, then find p:

B solves it like this:

The chance that a head comes up on an even toss is:

Now sum that series:

Set the sum to 2/5 and solve for p.

Solve the equation any way you can, to get p = 1/3

Has B solved the problem?

Of course she has!

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

Hi bobbym,

*Last edited by gAr (2012-07-11 19:13:52)*

"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: 86,730

Hi gAr;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

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

Hi bobbym,

"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: 86,730

Hi gAr;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

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

Hi,

"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: 86,730

Hi gAr;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

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

Hi,

I think we are not doing the same thing.

Suppose we throw the dice 4 times, (1,4), (5,3), (5,6), (2,3), we are taking absolute value of the difference? |(1+5+5+2)-(4+3+6+3)| = |13-16| = 3

Are we estimating the difference like that on the long run?

"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: 86,730

Yes, that is what my example indicates. When I see a nice solution I get too excited and rush to post it. This has hurt me before and I must learn to slow down. To post it when I am sure I understand what was shown to me.

If we add the numbers like that the difference will approach zero. The expected value of both die will be 3.5.

I did not show the correct way to subtract the die!

(3,6) = 3

(5,1) = 4

(3,3) = 0

(5,6) = 1

(3+4+0+1) = 8

That is the correct way. Pairwise!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

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

"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: 86,730

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

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

Hi bobbym,

*Last edited by gAr (2012-07-12 00:15:04)*

"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: 86,730

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

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

Hi,

But we are considering abasolute values, it must be increasing, isn't it?

"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: 86,730

Hi;

I am pretty sure even with the absolute value the expected difference between 2 die can never be more than 5. (6,1) being the maximum. That is what this guys formula indicates. If I am wrong here it is because I did not present the problem correctly.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

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

Yeah, the way I understand the problem leads me nowhere else.

Perhaps you could post a code in procedural manner for simulation, so that I may understand the actual question?

"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: 86,730

Hi gAr;

Okay, let's put into a form that we both agree on and gets the same answer he got. Do not worry I will send you the page when we are done so you can see what Robert Israel did without my interpretation getting in the way.

Here is the algorithm:

1)Pick two random integers in the interval [1,6].

2)Subtract them and take the absolute value.

3)Take the average of all of those values.

4) Print the answer.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**