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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,193

Hi gAr;

I feel 6 and 8 are the easier ones, relatively.

Completed 6, but it was not easy for me. Will post it as soon as I latex it up.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

hi gAr

the answer would be much prettier if you put 9999 instead of 999.

*Last edited by anonimnystefy (2011-08-04 23:59:32)*

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

The knowledge of some things as a function of age is a delta function.

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

Hi bobbym,

Okay, let us see.

Hi anonimnystefy,

That answer is pretty enough! The prettiest is only when the upper limit is 'n'. Anyway, good job!

"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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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

thanks! keep up the good problems.

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

The knowledge of some things as a function of age is a delta function.

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

You're welcome.

There are still some for you to try.

"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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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

i saw them but they look too hard for me.

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

The knowledge of some things as a function of age is a delta function.

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

Some questions just require some transformation, then they easily telescope.

"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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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

hi gAr

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

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,193

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

**Online**

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

Hi anonimnystefy,

"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: 104,193

Hi gAr;

Did you see mine, I nearly ran out of cyber ink. But at least I got a refresher course on the discrete calculus.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

**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: 104,193

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.**

**Online**

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

Hi,

No problem, counts as another solution. I haven't done a problem on discrete calculus, though!

But it must have cost you much time to type the solution, 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: 104,193

Hi gAr;

About twice as long as it took to do the problem. Then when I was almost done there was a sign error that almost went undiscovered.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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

Hi,

Okay.

"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: 104,193

Hi gAr;

Thanks for the problems.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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

You're welcome!

"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

**9)**

"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

**10) **

Prove that

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

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**reconsideryouranswer****Member**- Registered: 2011-05-11
- Posts: 171

9)

Signature line:

I wish a had a more interesting signature line.

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**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: 104,193

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

**Online**

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

Hi bobbym,

Did you? Answer looks awesome!

"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: 104,193

Not yet gAr, it was the suggestion I was applauding. People taught math today have been so conditioned that trying numbers or even guessing at a solution is somewhat evil. They keep mentioning a few offhand problems where some guy tried a thousand numbers and they worked but failed for the 10 millionth number. What they forget is all the problems ( a far larger number by the way ) where getting a solution to fit 1000 numbers worked!

Experimental play can at least provide insight into what a solution might be. With todays computing power this process is easy.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

**Online**