Questions tagged [integer-partitions]
For challenges related to the different ways of expressing an integer as a sum of positive integers.
24
questions
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 ...
- 42.2k
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
...
- 57.4k
2
votes
8
answers
1k
views
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,...
- 4,342
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 ...
- 100k
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 ...
- 421
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 ...
- 194k
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, ...
- 7,219
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 ...
- 2,299
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 ...
- 194k
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
...
- 28.4k
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 ...
user70974
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 ...
- 1,131
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 ...
- 17.6k
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 ...
- 323
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,\...
- 64.8k
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 ...
- 2,609
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 ...
- 461
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 ...
- 194k
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, ...
- 381
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 ...
- 363
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,...
- 295
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 ...
- 21.2k
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 ...
- 5,321
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:
...
- 219