• #### Re: cotpi 55 - Partitioning an integer and its double

From henhanna@gmail.com@21:1/5 to cotpi on Sun Sep 18 14:03:35 2022
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

number of possible partitions of 2n into n parts

e.g.
4 into 2 parts ==> (3,1) (2,2)

6 into 2 parts ==> (5,1) (4,2) (3,3)

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• From henhanna@gmail.com@21:1/5 to cotpi on Sun Sep 18 14:09:14 2022
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

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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• From henhanna@gmail.com@21:1/5 to henh...@gmail.com on Mon Sep 19 10:05:00 2022
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 !

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)

i'd love to see Other problems about Partitions !

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