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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12 votes
19 answers
964 views

Restricted Integer Partitions

Pk(n) means the number of partitions of n into exactly k parts. Given n and ...
19 votes
21 answers
2k views

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 ...
31 votes
30 answers
8k views

Chicken McNugget Numbers

Description Chicken McNugget numbers are numbers that can be expressed as a sum of \$6\$, \$9\$ or \$20\$ - the initial sizes of the famous Chicken McNuggets boxes sold by McDonald's. In that sum, a ...
22 votes
18 answers
2k views

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 ...
11 votes
19 answers
1k 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: ...
34 votes
25 answers
3k views

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, ...
37 votes
29 answers
3k views

This Challenge Makes Cents

I know, the title cracks you up Given an amount of money, output the fewest number of coins that make up that amount. Examples ...
71 votes
26 answers
9k views

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 ...
26 votes
6 answers
2k views

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 ...
15 votes
3 answers
341 views

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 ...
18 votes
14 answers
3k views

Landau logarithm

Related: Landau's function (OEIS A000793) Background Landau's function \$g(n)\$ is defined as the largest order of permutation of \$n\$ elements, which is equal to \$\max(\operatorname{lcm}(a_1,a_2,\...
14 votes
24 answers
2k views

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 ...
3 votes
7 answers
385 views

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 - ...
10 votes
6 answers
479 views

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 ...
19 votes
10 answers
2k views

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 ...
22 votes
16 answers
1k views

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 ...
15 votes
10 answers
780 views

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 ...
28 votes
27 answers
2k views

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, ...
20 votes
12 answers
1k views

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 ...
15 votes
5 answers
931 views

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: ...
16 votes
11 answers
1k 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 ...
26 votes
9 answers
1k views

Minimally Making Change

This problem is an extension of what happens to me on a regular basis: I have to have $1.00 in coins and have to be able to give change to somebody. I discovered rather quickly that the ideal coins to ...
12 votes
6 answers
1k views

Darts meets Codegolf

I think everyone is familiar with the game of darts. For those that don't understand the scores, here is a useful link. The board A dartboard can be compared to a pie cut in 20 pieces. Each piece is ...
39 votes
18 answers
7k views

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 ...
16 votes
16 answers
3k views

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 ...
13 votes
4 answers
1k views

I ain't no Fortunate sum

The primorial \$p_n\#\$ is the product of the first \$n\$ primes. The sequence begins \$2, 6, 30, 210, 2310\$. A Fortunate number, \$F_n\$, is the smallest integer \$m > 1\$ such that \$p_n\# + m\$ ...
19 votes
11 answers
2k views

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 ...
7 votes
11 answers
489 views

Constrained integer partition

Challenge In this challenge, all numbers are in \$\mathbb{N}_0\$. Create a function or program that, when given a number \$N\$ and a tuple of \$k\$ numbers \$(n_i)\$ (all ≤ \$N\$), returns the number ...
21 votes
6 answers
408 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 ...
18 votes
13 answers
640 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\$ positive integer parts,...
49 votes
14 answers
4k views

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 ...
13 votes
4 answers
570 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: ...
8 votes
3 answers
251 views

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 ...
21 votes
12 answers
3k views

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 ...
16 votes
11 answers
2k views

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 ...
4 votes
5 answers
225 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 ...
19 votes
37 answers
3k views

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 ...
17 votes
3 answers
496 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 ...
16 votes
10 answers
2k views

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 ...
18 votes
7 answers
634 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 ...
19 votes
15 answers
3k views

The minimum fibonacci challenge!

Challenge In this task you would be given an integer N (less than 106), find the minimum way in which you could sum to N using only Fibonacci numbers - this partition is called Zeckendorf ...
33 votes
24 answers
4k views

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, ...
24 votes
12 answers
2k views

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 ...
23 votes
27 answers
2k views

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 ...
7 votes
6 answers
365 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 ...
12 votes
11 answers
875 views

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 ...
21 votes
20 answers
6k views

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 ...
4 votes
0 answers
73 views

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 ...
27 votes
10 answers
1k views

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. ...
17 votes
4 answers
3k views

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 ...