# Questions tagged [integer-partitions]

For challenges related to the different ways of expressing an integer as a sum of positive integers.

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### Multigraphs with a given degree sequence

This challenge will give you an input of a degree sequence in the form of a partition of an even number. Your goal will be to write a program that will output the number of loop-free labeled ...
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### Calculate Landau's function

Landau's function $g(n)$ (OEIS A000793) gives the maximum order of an element of the symmetric group $S_n$. Here, the order of a permutation $\pi$ is the smallest positive integer $k$ such ...
198 views

### Is there are exactly one partition, given length of partition and maximum number?

It is Restricted Integer Partitions, but with maximum number. Question Three positive integers are given. First number is number to divide, second number is length of partition, and third number is ...
438 views

### Optimize my wings order

This tweet lists the possible orders for Wings of a Chinese restaurant1: When ordering Pizza I usually calculate what size gives me the best Pizza-price ratio which is a simple calculation. However ...
624 views

### Split the bits!

We define $V(x)$ as the list of distinct powers of $2$ that sum to $x$. For instance, $V(35)=[32,2,1]$. By convention, powers are sorted here from highest to lowest. But it does not affect ...
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### Sum of five cubes

Given an integer, output five perfect cubes whose sum is that integer. Note that cubes can be positive, negative, or zero. For example, ...
857 views

### Sum of combinations with repetition

Write the shortest code you can solving the following problem: Input: An integer X with 2 <= X and X <= 100 Output: ...
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### Write numbers as a difference of Nth powers

Challenge There are many numbers which can be expressed as the difference of two squares, or as the difference of two cubes, or maybe even higher powers. Talking about squares, there are various ways ...
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### Find the largest number of distinct integers that sum to n

The Task Given an input positive integer n (from 1 to your language's limit, inclusively), return or output the maximum number of distinct positive integers that ...
333 views

### Count of relatively prime partitions

The partitions of an integer N are all the combinations of integers smaller than or equal to N and higher than 0 which sum up to N. A relatively prime partition is an integer partition, but whose ...
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### Yo boy, must it sum

Every positive integer can be expressed as the sum of at most three palindromic positive integers in any base b≥5.   Cilleruelo et al., 2017 A positive integer is palindromic in a given base if ...
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### How many partitions do I have?

The partition number of a positive integer is defined as the number of ways it can be expressed as a sum of positive integers. In other words, the number of integer partitions it has. For example, the ...
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### Self-summed numbers

Convert a number to a sum of digits Not any sum: we need the shortest sum Not any digits: you can use only digits of the number Example You will be given as input an integer ...
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### Restricted Integer Partitions

Pk(n) means the amount of partitions of n into exactly k parts. Given n and ...
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### Fewest operations to 100

Overview Given a list of digits, find the fewest operations to make 100 Input A string of digits, which may or may not be in numerical order. The order of the digits cannot be changed, however plus ...
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### 11 = (1+2+3+4+5) - (1+2+3) + (6) - (4)

Given a positive integer N, your task is to return the number of steps required by the following algorithm to reach N: Find the smallest triangular number Ti such that Ti ≥ N. Build the ...
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### Code Golf - Print all unique ways of writing a number as a sum with a lexical order [duplicate]

I found about Code Golf after writing this program and decided to post the rules here so you can try it out too. I saw this, which is a less restrictive version of my question. I've got a bit more ...
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### A penny saved is a penny

...counted! You will pass your program a variable which represents a quantity of money in dollars and/or cents and an array of coin values. Your challenge is to output the number of possible ...
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### List all ordered partitions of n

The challenge is to list all ordered partitions (composition (combinatorics)) of a given positive integer n. These are the lists of numbers from ...
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### Calculate the partitions of N

Your challenge is simple: GIven an integer N, ouput every list of positive integers that sums to N. For example, if the input was 5, you should output ...
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### Strict partitions of a positive integer

OEIS A000009 counts the number of strict partitions of the integers. A strict partition of a nonnegative integer n is a set of positive integers (so no repetition ...
384 views

### Partitioning reciprocals

Given a number n > 77, write a program or function that finds a set of distinct positive integers such that the sum of the set equals n, and the sum of the reciprocals of the set equals 1. Example ...
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### Sums of Consecutive Integers

Before anyone says anything, similar and similar. But this is not a dupe. Some positive integers can be written as the sum of at least two consecutive positive integers. For example, ...
859 views

### Minimum number of numbers to sum to exactly n

First question here, don't yell at me if this is a duplicate or a bad challenge. Introduction I thought of this challenge myself, and it seems to be a good basic puzzle for beginner code-golfers. It ...
601 views

### Find the sets of sums

I've enjoyed reading this site; this is my first question. Edits are welcome. Given positive integers n and m, compute all ordered partitions of m into exactly n parts positive integer parts, and ...
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### Hook length product

A Young diagram is an arrangement of boxes in left-justified rows and top-justified columns. For each box, all the spaces above it and to its left are occupied. ...
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### Fissile Numbers

I found this sequence while working on Evolution of OEIS, but never got around to posting it as an answer. After writing a reference implementation in Mathematica, I thought this is a fun exercise to ...
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### Build an ASCII Fibonacci Clock

Someone built a really fancy clock using Fibonacci numbers, which looks really nice but is fairly unusable. Just the way we like it! Let's recreate this. The clock is made up of 5 sections ...
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### Random Golf of the Day #3: Integer Partitions

About the Series First off, you may treat this like any other code golf challenge, and answer it without worrying about the series at all. However, there is a leaderboard across all challenges. You ...
522 views

### Nearest partition numbers

The number of partitions of an integer is the number of ways that integer can be represented as a sum of positive integers. For example: ...
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### Compute the number of ways how you can express a number as a sum [closed]

For a given natural number n, compute the number of ways how one can express n as a sum of positive natural numbers. For example,...