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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

Hi;

**We have the multiset**

**s ={1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 5, 7, 7, 8, 9, 10, 10, 10, 10, 10}**

**and C has been busy trying to answer a question. So C brings it into the group because he thinks he has the right answer.**

**What is the number of partitions of s that add up to 17? C has an answer of 91.**

**A says) It is a lot higher than that C. A few minor mathematicians like De Moivre worked on these partition problems but it was finally the great Euler that told us everything about them. Incidentally, did I tell you fellows that the blood of Euler courses through my veins? Yes, I am related to him.**

**B says) It is lower not higher and why do you think De Moivre was a minor mathematician? Did you know that Newton would bring his probability problems to De Moivre?**

**C says) Those were handouts B and I had a hunch the answer was higher.**

**D says) Who is Euler?**

**E says) You are partially right C, Newton was trying to give him some work but only because he saw that he was great mathematician and Newton respected that. Also A, B is right, it is lower. Looks like all that Euler blood leaked out of you.**

**A says) It is higher bumpkin!**

**What do you say?**

**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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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 563

Hello:

*Last edited by ElainaVW (2014-03-21 14:24:52)*

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What is a multiset? What do you mean by a partition of s?

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

A multiset is used in combinatorics a lot. They are sometimes called families too. They are sets that are allowed to have duplicates.

A partition of a number is a way to write a number as a sum of other numbers.

1 + 5 = 6

1 + 1 + 4 = 6

1 + 2 + 3 = 6

Are all partitions of 6. They are similar to compositions except order does not count. 1 + 2 + 3 and 3 + 1 + 2 are considered to be the same.

**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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You explained partitions of a number. But what are partitions of a multiset? Are they subsets 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'

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

They are like restricted partitions. The partitions must come from the multiset.

s ={1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 5, 7, 7, 8, 9, 10, 10, 10, 10, 10}

1 + 1 + 1 + 1 + 2 + 2 + 8 is a restricted partition of 17 while

1 + 1 + 1 + 1 + 1 + 2 + 10 is not.

**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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Are you asking to find the number of submultisets of s whose sum of elements is 17?

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

Yes but there is no need for the usage of that name, we call them partitions.

**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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Did you notice something?

'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: 106,389

I missed replying to a solution.

**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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Is A claiming that Euler is a higher bumpkin.

'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: 106,389

A is claiming something, I am not sure what it is.

**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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Can we have A on the forum?

'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: 106,389

Hmmmm, why do we want him?

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

Hi bobbym,

"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: 106,389

Hi gAr;

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

Thanks!

"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: 106,389

You are very welcome.

Have to go, see you later.

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

Okay, see you later..

"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: 106,389

Hi gAr;

Did you know there is no analytical answer for anything more then a spread of 2?

**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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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

Hi ShivamS;

**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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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

Hi;

**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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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

Wonderbar!

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