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

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,208

Hi;

There is a generating function solution to that one.

**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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Is it like multiplying two functions and then checking the coefficient of it....?

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,208

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.****If it ain't broke, fix it until it is.**

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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)*

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,208

We can answer quickly with 512.

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

Only joking... no offense

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,208

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.****If it ain't broke, fix it until it is.**

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Not good?? Then I am worse than worse.

Jokes apart ...... How do you do it?

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,208

Do what? Stumble around? It 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.**

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Stumble around?

I mean, how did you do the problem?

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,208

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.****If it ain't broke, fix it until it is.**

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May I see your program?

Sunsets? Sounds nice

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

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,208

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

Returns 512

**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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!!!!!!!!!

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,208

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.****If it ain't broke, fix it until it is.**

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Yep veryyy strange

Getting a little clear though

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,208

You can try it at Alpha.

**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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The website?

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

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,208

Yes, they let you use Mathematica there.

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

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.

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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Hmm...

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

What is it?

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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I mean I understood TY

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

You are welcome!

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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