# 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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### Help me design an unfair laundry machine

There's a payment machine for laundry in my building which does a few frustrating things. The ones relevant to this challenge are: It doesn't make change. So if you pay over the amount then you are ...
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### There's more than one way to skin a set

Given a set of positive integers $S$, output the set of all positive integers $n$ such that $n$ can be made by summing a subset of $S$ in more than one different way, i.e., that are ...
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### Split given integer into a given number of integers, each within given bounds

Input variables: (Names are just examples, they don't need to be named like this) GrandTotal - integer to divide SplitCount - ...
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### Mirror an integer... in NDos' way

NDos' Numeral System NDos' numeral system is a numeral system invented by me. It represents every nonnegative integer by a binary tree. Given a nonnegative integer $n$: If $n=0$, it is ...
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### 1 bit, 2 bits, 3 bits, …

Given a positive integer $n$, your task is to find out the number of partitions $a_1+a_2+\dots+a_k=n$ where each $a_j$ has exactly $j$ bits set. For instance, there are $6$ such partitions ...
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### AoCG2021 Day 14: Adjusting dancing program's period

Part of Advent of Code Golf 2021 event. See the linked meta post for details. Related to AoC2017 Day 16. I'm using the wording from my Puzzling SE puzzle based on the same AoC challenge instead of the ...
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### Minimally prepend numbers to get a symmetric Young diagram

Background A Young diagram is a diagram that represents a nonincreasing sequence of positive integers using left-justified rows of squares. As an example, 5, 4, 1 ...
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### Non-sums of distinct positive powers

There are 31 positive integers that cannot be expressed as the sum of 1 or more distinct positive squares: ...
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### Display a number in Toki Pona

Toki Pona is a constructed language with 137ish words, designed to constrain the speaker to expressing ideas in a simple and straightforward manner, reducing ideas to more essential forms. Often, ...
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### List array elements which can be summed from other elements

Consider an array of unique integers, with an arbitrary length greater than 2. It is sometimes possible to express elements of the array as the sum of at least two other elements. For example, if our ...
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### Number of coins needed to make change

Relatable scenario: I'm going to the store to buy a single item, but only have a $100k bill. As a result, I need exactly$99,979 in change, and in the fewest coins/bills possible because I'm quite ...
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### The Coin Problem

Background The official currency of the imaginary nation of Golfenistan is the foo, and there are only three kinds of coins in circulation: 3 foos, 7 foos and 8 foos. One can see that it's not ...
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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 ...
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### 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: ...