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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Restricted Integer Partitions
Pk(n) means the number of partitions of n into exactly k parts. Given n and ...
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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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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 ...
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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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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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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, ...
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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
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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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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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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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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,\...
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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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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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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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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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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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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 ...
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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 ...
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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 ...
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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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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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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\$ ...
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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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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 ...
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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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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,...
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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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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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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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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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 ...
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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,
...
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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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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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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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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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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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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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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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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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