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Jun 28, 2012, 4:48:00 PM6/28/12

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A partition of a positive integer n is a list of positive

integers, ordered from largest to smallest, such that the sum of

the integers in the sequence is n. Each integer in the list is

called a part.

What is the ratio of the number of possible partitions of a

positive integer n to the number of possible partitions of 2n

into n parts?

--

Originally posted at: http://cotpi.com/p/55/

Correct solutions will be archived at the URL mentioned above.

Solutions to 'Gambling with a die': http://cotpi.com/p/54/#solutions

integers, ordered from largest to smallest, such that the sum of

the integers in the sequence is n. Each integer in the list is

called a part.

What is the ratio of the number of possible partitions of a

positive integer n to the number of possible partitions of 2n

into n parts?

--

Originally posted at: http://cotpi.com/p/55/

Correct solutions will be archived at the URL mentioned above.

Solutions to 'Gambling with a die': http://cotpi.com/p/54/#solutions

Jun 28, 2012, 5:26:53 PM6/28/12

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Each partition of 2n into n parts contains numbers in the range 1 to n

+1.

Subtracting 1 from each number and discarding the 0s thus results in a

partition of n.

Conversely, any partition of n contains 1 to n numbers. Adding 0s to

partitions with less than n numbers to bring up the total to n and

then adding 1 to each number results in a partition of 2n into n

parts.

Thus the ratio is 1.

Please reply to ilan dot mayer at hotmail dot com

__/\__

\ /

__/\\ //\__ Ilan Mayer

\ /

/__ __\ Toronto, Canada

/__ __\

||

Message has been deleted

Sep 18, 2022, 5:09:16 PMSep 18

to

4 into 2 parts ==> (3,1) (2,2)

WRONG> 6 into 2 parts ==> (5,1) (4,2) (3,3) <True but Not relevant to the Prob.

6 into 3 parts ==> (4,1,1) (3,2,1) (2,2,2)

Sep 19, 2022, 1:05:03 PMSep 19

to

On Sunday, September 18, 2022 at 2:09:16 PM UTC-7, henh...@gmail.com wrote:

> On Thursday, June 28, 2012 at 1:48:00 PM UTC-7, cotpi wrote:

> > A partition of a positive integer n is a list of positive

> > integers, ordered from largest to smallest, such that the sum of

> > the integers in the sequence is n. Each integer in the list is

> > called a part.

> >

> > What is the ratio of the number of possible partitions of a

> > positive integer n to the number of possible partitions of 2n

> > into n parts?

> >

> > --

> > Originally posted at: http://cotpi.com/p/55/

> > Correct solutions will be archived at the URL mentioned above.

> >

> > Solutions to 'Gambling with a die': http://cotpi.com/p/54/#solutions

>

>

this is a NICE problem !
> On Thursday, June 28, 2012 at 1:48:00 PM UTC-7, cotpi wrote:

> > A partition of a positive integer n is a list of positive

> > integers, ordered from largest to smallest, such that the sum of

> > the integers in the sequence is n. Each integer in the list is

> > called a part.

> >

> > What is the ratio of the number of possible partitions of a

> > positive integer n to the number of possible partitions of 2n

> > into n parts?

> >

> > --

> > Originally posted at: http://cotpi.com/p/55/

> > Correct solutions will be archived at the URL mentioned above.

> >

> > Solutions to 'Gambling with a die': http://cotpi.com/p/54/#solutions

>

>

i'll check out his (her) other problems

> > number of possible partitions of 2n into n parts

> e.g.

> 4 into 2 parts ==> (3,1) (2,2)

>

>

> WRONG> 6 into 2 parts ==> (5,1) (4,2) (3,3) <True but Not relevant to the Prob.

>

> 6 into 3 parts ==> (4,1,1) (3,2,1) (2,2,2)

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