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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 580

A person picks from the set of numbers {1,2,3,...100} eighty of them without replacement that sum to 3690. In how many ways can they do that?

Merry Christmas to everyone!

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 580

That's right. How did you get it?

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

EM of course?! What a silly question.

I have one too.

The numbers from 1 to 13 are sorted in a list like this {1,2,3,4,5,6,7,8,9,10,11,12,13}. A person comes over and picks a random number from 7 to 12 inclusive. He then cuts the list at that number like this

{1,2,3,4,5,6,7,8,9,10,11,12,13}

random number he picks is 9, so he cuts the list like this

{10,11,12,13} and {1,2,3,4,5,6,7,8,9} and merges the two lists into 1 list again.

{10,11,12,13,1,2,3,4,5,6,7,8,9}

It was so much fun he does it again:

{10,11,12,13,1,2,3,4,5,6,7,8,9}

random number = 7 he again breaks the list into

{4,5,6,7,8,9} and {10,11,12,13,1,2,3}

and again he merges this into 1 big list

{4,5,6,7,8,9,10,11,12,13,1,2,3}

he repeats this process again and again and then he gets a thought. What is the expected number of times he must do this for the list to come back to {1,2,3,4,5,6,7,8,9,10,11,12,13}?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 580

Hello:

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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