Tool to generate partitions of a number (integer). A partition of an integer N is a decomposition of N into a set of numbers (inferior to N) which sum is N.

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day! You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? Contact-me!

Tool to generate partitions of a number (integer). A partition of an integer N is a decomposition of N into a set of numbers (inferior to N) which sum is N.

Answers to Questions

What is a partition of an integer number?

Definition: in mathematics, a partition \( p(N) \) of a number N is a set of numbers (less than or equal to N) whose addition is N.

Example: The number \( 5 \) can be decomposed into \( 7 \) distinct partitions : \( 5, 4+1, 3+2, 3+1+1, 2+2+1, 2+1+1+1, 1+1+1+1+1 \)

Permutations are ignored: \( 4+1 \) and \( 1+4 \) are considered identical

Example: The number \( 10 \) has \( 42 \) partitions, and the number \( 100 \) has \( 190569292 \).

Due to computation cost with large lists, free generations are limited.

What is the Hardy-Ramanujan formula?

In 1918, Hardy and Ramanujan have found an approximation od \( p(n) \) for big numbers \( n \) :

Partitions of a number are used to solve the change-making problem and to list the ways of give back money.

Example: There are 49 ways to make $ 100 with $ 5, $ 10, $ 20 or $ 50 notes

How remove the limits of the generator?

The generation is very costful in resources (which are expensive) as soon as the quantity of solution becomes large. dCode offers exhaustive lists, ask for prices !

Ask a new question

Source code

dCode retains ownership of the source code of the script Number Partitions online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be given for free. So if you need to download the online Number Partitions script for offline use, check contact page !