Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #151 2013-01-15 22:49:31

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

### Re: A few questions

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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## #152 2013-01-16 01:38:35

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,035
Website

### Re: A few questions

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'
I'm not crazy, my mother had me tested.

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## #153 2013-01-16 02:19:04

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

### Re: A few questions

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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## #154 2013-01-16 14:15:39

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,035
Website

### Re: A few questions

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'
I'm not crazy, my mother had me tested.

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## #155 2013-01-17 03:53:50

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

### Re: A few questions

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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## #156 2013-01-17 14:27:28

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,408

### Re: A few questions

Hi Agnishom;

What is the title pf the book?

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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## #157 2013-01-18 01:46:15

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,035
Website

### Re: A few questions

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'
I'm not crazy, my mother had me tested.

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## #158 2013-01-18 01:54:18

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

### Re: A few questions

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

"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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## #159 2013-01-18 02:00:04

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,035
Website

### Re: A few questions

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

'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'
I'm not crazy, my mother had me tested.

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## #160 2013-01-18 04:37:40

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,408

### Re: A few questions

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.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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## #161 2013-01-18 15:00:08

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,035
Website

### Re: A few questions

Hi bobbym;

Get Well soon

See this website.
and this as well

'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'
I'm not crazy, my mother had me tested.

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## #162 2013-01-18 16:09:30

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,408

### Re: A few questions

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.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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## #163 2013-01-18 16:12:51

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

### Re: A few questions

Hi bobbym,

How are you now?

Hi Agnishom,

"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."

Offline

## #164 2013-01-18 16:16:15

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,408

### Re: A few questions

Hi gAr;

Not much better, kind of tired.

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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## #165 2013-01-18 16:23:43

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

### Re: A few questions

Hi,

Oh, take some rest..

"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."

Offline

## #166 2013-01-18 16:40:39

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,408

### Re: A few questions

Hi;

That is what I am going to do.

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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## #167 2013-01-19 01:52:36

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,035
Website

### Re: A few questions

bobbym wrote:

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

Regarding what?

'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'
I'm not crazy, my mother had me tested.

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## #168 2013-01-19 13:16:11

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,408

### Re: A few questions

Hi Agnishom;

Solutions for RMO's and that sort of thing.

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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## #169 2013-02-09 14:29:45

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,035
Website

### Re: A few questions

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

'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'
I'm not crazy, my mother had me tested.

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## #170 2013-02-09 14:53:51

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,408

### Re: A few questions

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)

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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## #171 2013-02-09 20:29:00

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,035
Website

### Re: A few questions

Actually, they said "without using a calculator"

'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'
I'm not crazy, my mother had me tested.

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## #172 2013-02-09 21:03:01

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

### Re: A few questions

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

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## #173 2013-02-09 22:33:10

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,408

### Re: A few questions

Hi;

You can also get quite close using:

$\large \bold{ 5^{44}= \frac{10^{44}}{\left ( 2^{10} \right )^4 \cdot 2^4}}$

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

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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## #174 2013-02-10 01:41:03

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,035
Website

### Re: A few questions

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?

'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'
I'm not crazy, my mother had me tested.

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## #175 2013-02-10 01:45:06

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

### Re: A few questions

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

Offline