# 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### Partition of a positive integer N [closed]

Find the number of partitions of a positive integer n. Hope someone uses the explicit finite formula for the partition function defined in Jan Hendrik Brunier and Ken Ono paper here. ...
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