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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,383

Hi Avon;

bobbym, I apologise if I have caused any offence

No need for an apology I was not offended, I just wanted Agnishom to know I was not annoyed or put off that he was asking questions about the alleged proof. As you stated he was correct is asking for more.

I think you are missing something.

Hmmm, since the day I was born that has been true. You are correct, the hole in my reasoning is in 2). I thought I could get around that and thus leave out the derivation as he supplied in 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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

bobbym wrote:

Hi;

Call there ages a,b,c,d.

There are four girls needed to make 6 pairs.

Hi bobbym

That isn't the only solution.

*Last edited by anonimnystefy (2012-12-03 21:59:17)*

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: 85,383

Hi;

Are you sure about that?

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

Yes.

Did ypu try permutating the rhs' of those equations?

*Last edited by anonimnystefy (2012-12-03 22:07:47)*

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: 85,383

Yes, but that would only change the order. Since the assignments of a,b,c,d is arbitrary the order does not count. No matter how we permute it the 4 girls ages are the same.

**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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,844

Hi all,

Here's what I did...

There are only 6 possible pairings, as follows:

a + b = 30

a + c = 33

a + d = 41

b + c = 58

b + d = 66

c + d = 69

From this, 3a + 3b + 3c + 3d = 297

Substituting (to leave one variable...for which I chose d):

123 - 3d + 198 - 3d + 207 - 36 + 3d = 297

6d = 231

d = 38.5

Substituting that result to find the other ages:

a = 41 - d = 41 - 38.5 = 2.5

b = 66 - d = 66 - 38.5 = 27.5

c = 69 - d = 69 - 38.5 = 30.5

It seems to me that they're the only solutions.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,383

Hi phrontister;

Did you see my post #24?

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

Combinatorics is Algebra and Algebra is Combinatorics.

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Hmm... I also tried doing it on my own

But I was confused.

However, Thank You!

'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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,844

Hi Bobby,

Yes, I did, but as I didn't know how you got to your answer I thought I'd give it a try with the little I know.

I suppose there's some other way of doing this that conforms to the other posts in the thread...which I didn't follow, as I don't think I've done this type of problem before.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,383

Hi;

I am super busy with another problem so I have not had time to check. Does your solution agree with mine?

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,844

Yes, exactly the same. The only difference is that yours are fractions and mine are decimal.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,383

Okay, thanks for checking. I think Mr. Agnishom's question has been answered.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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My answers match too....

This one is very basic but I am not aware of the basic concepts used

Question 4:**Find the remainder when 21990 is divided by 1990.**

'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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,844

Hi Bobby,

Yes, I thought you probably answered it but I don't know enough about this topic to know that for sure. I was just throwing my tuppence-worth into the ring in case it might mean something to someone.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,383

Hi phrontister;

I do not mind at all.

Hi Agnishom;

That is a modulo operation.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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Yes I know it is called a modulo operation, .... How do you tackle it?

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,383

When they are both positive like that the simplest way is

take the integer part of the answer which is 11.

We say:

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,844

Here's how I think about it:

I'll let bobbym explain modulo. I know what it does, but I forget why.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,383

Hi phrontister;

Sometimes when the numbers are small successive subtraction is fastest. Of course Mathematica has a built in function.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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I am terribly embarassed about it

I meant to say:

Find the remainder when

is divided by 1990

'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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,844

Hi Bobby,

I've only comparatively recently started thinking 'floor function' instead of 'integer'...and I also only use the dot instead of the multiplication sign rarely.

My instinct was to write the equation in my previous post as

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,844

Hi Agnishom,

Actually, from what I see of how you typed that into your post, you meant this:

Find the remainder when

is divided by 1990.But I'm off to bed now (very early start in the morning), so I'll leave the answer to others.

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Yes sorry Please don't mind

I have some problems with tackling that latex

'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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**scientia****Member**- Registered: 2009-11-13
- Posts: 222

*Last edited by scientia (2012-12-04 04:44:11)*

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scientia wrote:

We also know that

since

Will you please explain this line?

'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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