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

Hi Agnishom,

*Last edited by gAr (2013-01-15 22:51:14)*

"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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Thnk you gAr

One question, if I get such a question in an exam shall I have to write out all the possible combinations?

*Last edited by Agnishom (2013-01-16 01:42:40)*

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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

Hi,

I think you can only mention about the remainders, number of such combinations and the pigeonhole principle.

But I'm a bit confused about the minimum of such numbers required to guarantee that no three numbers form a cube, because we can see that taking three consecutive numbers there is also a cube.

Anyway, a good question, is it from a question paper?

"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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Yes. It is

*Last edited by Agnishom (2013-01-16 14:21:40)*

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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

Ok, thanks for the questions..

"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: 86,161

Hi Agnishom;

What is the title pf the book?

**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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Title pf means?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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

I think he typed "pf" instead of "of"..

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

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Well

I am not taking them from a book instead I am asking them from various olympiad questions

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

Hi gAr and Agnishom;

I have the flu and I am not as sharp as usual. I did mean of, sorry.

What I meant is Olympiad problems have numbers and state what Olympiad they are from. They also have answers to them that I can look up so you can study them. gAr's answer is the one I was working on also but he got there first.

**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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'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

Hi Agnishom;

I have downloaded some more pdfs but so far nothing to help us.

**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

Hi bobbym,

How are you now?

Hi Agnishom,

Thanks for the links.

"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: 86,161

Hi gAr;

Not much better, kind of tired.

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

Hi,

Oh, take some rest..

"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: 86,161

Hi;

That is what I am going to do.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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bobbym wrote:

I have downloaded some more pdfs but so far nothing to

helpus.

Regarding what?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

Hi Agnishom;

Solutions for RMO's and that sort of thing.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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Question 11: **How many digits does 5^44 have?**

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

10^x = 5^44

Take the common log of both sides

x = 44 log(5)

x = 30.7546

So we have

10^(.7546) * 10 ^30

5.48 * 10^30 moves the decimal point 30 places to the right. So it has 31 digits.

*Last edited by bobbym (2013-02-09 15:25:40)*

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

Combinatorics is Algebra and Algebra is Combinatorics.

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Actually, they said "without using a calculator"

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

Hi Agnishom

You can still use that.

The number of digits of a number is floor(log_10(that number))+1.

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: 86,161

Hi;

You can also get quite close using:

*Last edited by bobbym (2013-02-09 23:19:13)*

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

Combinatorics is Algebra and Algebra is Combinatorics.

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anonimnystefy wrote:

Hi Agnishom

You can still use that.

The number of digits of a number is floor(log_10(that number))+1.

Thats correct

Now, how do I do that to 5^44 without a calculator?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

Well you can approximate the logarithm...

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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