Questions tagged [integer-partitions]
For challenges related to the different ways of expressing an integer as a sum of positive integers.
61 questions
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Pennies to Dollars
Over on Puzzling a couple years ago, Hermant Agarwal proposed the following question:
In a certain country the following coins are in circulation: 1 cent, 2 cents, 5 cents, 10 cents, 20 cents, 50 ...
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How many chains?
Given a positive integer \$n\$, a partition of \$n\$ is an ascending sequence of numbers that sum to \$n\$.
Given two partitions \$a\$ and \$b\$, \$a\$ is a refinement of \$b\$ iff \$b\$ can be ...
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Superimposed triangles
Because \$k^2\$ is the sum of the \$k\$ first odd positive integers, squared numbers can be represented as ASCII-art triangles of height \$k\$ as follows:
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Binary expansion and partition numbers [closed]
Not sure if it's correct to ask such a question on this site, but let's try.
Let a(n) be a sequence of positive integer such that a(1) = 1. To reproduce the sequence a(n) through itself, use the ...
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Write a number as a sum of Fibonacci numbers
In 2009, Hannah Alpert described the "far-difference" representation, a novel way of representing integers as sums and differences of Fibonacci numbers according to the following rules:
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Best partitioning set
Given an array of \$n\$ positive integers we will say its self-sum order is the number of ways to add elements from it to make \$n\$. We will count ways as distinct up to associativity. So \$1+(2+3)\$...
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Count the number of compositions of \$n\$ in which the greatest part is odd
A composition of an integer \$n\$ is a representation of \$n\$ as a sum of positive integers. For example the eight compositions of 4 are as follows:
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user108721
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Number of ways to make an amount with coins
This is not a duplicate of Sum of combinations with repetition. This question considers 1+2 to be the same as 2+1. The other ...
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Sum of partition numbers
The partition function:
In number theory, the partition function p(n) represents the number of possible partitions of a positive integer n into positive integers
For instance, p(4) = 5 because the ...
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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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