Math Is Fun Forum

ElainaVW

Member

Registered: 2013-04-29

Posts: 580

Christmas Problem.

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!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Christmas Problem.

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.

ElainaVW

Member

Registered: 2013-04-29

Posts: 580

Re: Christmas Problem.

That's right. How did you get it?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Christmas Problem.

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.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Christmas Problem.

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{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.}

ElainaVW

Member

Registered: 2013-04-29

Posts: 580

Re: Christmas Problem.

Hello:

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Christmas Problem.

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.