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#1 2013-03-25 23:04:26

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,784
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The subset dilemma

Determine the number of subsets of A={1,2,…,10} whose sum of elements are greater than or equal to 28.


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#2 2013-03-25 23:17:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,438

Re: The subset dilemma

Hi;

There is a generating function solution to that one.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#3 2013-03-25 23:18:34

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,784
Website

Re: The subset dilemma

Is it like multiplying two functions and then checking the coefficient of 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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#4 2013-03-25 23:31:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,438

Re: The subset dilemma

Hi;

I do not know yet because I am not done with the other problems. Then I can concentrate on this one.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#5 2013-03-25 23:32:14

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,784
Website

Re: The subset dilemma

Maybe the original polynomial is x + x^2 + x^3 + ... + x^10

Then what to do with that?

Last edited by Agnishom (2013-03-25 23:40:54)


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#6 2013-03-25 23:39:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,438

Re: The subset dilemma

We can answer quickly with 512.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#7 2013-03-25 23:46:17

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,784
Website

Re: The subset dilemma

I know some fools who are good at math, but they won't tell me how they did it

Only joking... no offense


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#8 2013-03-25 23:55:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,438

Re: The subset dilemma

I am not offended. I am a fool who is not good at math.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#9 2013-03-26 00:06:11

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,784
Website

Re: The subset dilemma

Not good?? Then I am worse than worse.

Jokes apart ...... How do you do 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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#10 2013-03-26 00:15:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,438

Re: The subset dilemma

Do what? Stumble around? It is easy.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#11 2013-03-26 00:30:45

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,784
Website

Re: The subset dilemma

Stumble around?

I mean, how did you do the problem?


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#12 2013-03-26 00:41:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,438

Re: The subset dilemma

I am just intuitively guessing about the 512. There are 2^10 sunsets of those numbers. One to 10 sum to 55. 28 to 55 is half the numbers so it is a good guess about 1024 / 2 = 512.

I programmed it and that is the answer. Now I need a math way.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#13 2013-03-26 00:41:55

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,784
Website

Re: The subset dilemma

May I see your program?

Sunsets? Sounds nice

Last edited by Agnishom (2013-03-26 00:44:51)


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#14 2013-03-26 00:45:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,438

Re: The subset dilemma

Select[Total[#]&/@Subsets[Range[10]],#>27&]//Length

Returns 512


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#15 2013-03-26 00:56:53

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,784
Website

Re: The subset dilemma

!!!!!!!!!


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#16 2013-03-26 01:03:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,438

Re: The subset dilemma

It is a little strange to see a functional style of programming at first.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#17 2013-03-26 01:12:00

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,784
Website

Re: The subset dilemma

Yep veryyy strange
Getting a little clear though


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#18 2013-03-26 01:15:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,438

Re: The subset dilemma

You can try it at Alpha.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#19 2013-03-26 01:56:07

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,784
Website

Re: The subset dilemma

The website?

Last edited by Agnishom (2013-03-26 01:56:36)


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

#20 2013-03-26 02:02:37

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,438

Re: The subset dilemma

Yes, they let you use Mathematica there.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#21 2013-03-26 02:13:18

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,655

Re: The subset dilemma

It is half because if a set's sum of elements is >=28, then the sum of elements of its complement is <28. That means that there are as many subsets of the given set which have the element sum >=28 as there are with the element sum <28.


“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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#22 2013-03-26 03:58:06

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,784
Website

Re: The subset dilemma

Hmm...


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#23 2013-03-26 04:39:15

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,655

Re: The subset dilemma

What is it?


“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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#24 2013-03-26 04:54:51

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,784
Website

Re: The subset dilemma

I mean I understood TY smile


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

#25 2013-03-26 05:10:21

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,655

Re: The subset dilemma

You are welcome! smile


“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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