Questions tagged [math]
The challenge involves mathematics in some central way. Also consider using more specific tags, listed in the tag wiki info.
1,802
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Output a 1-2-3-5-7... sequence
Follow-up of my previous challenge, inspired by @emanresu A's question, and proven possible by @att (Mathematica solution linked)
For the purposes of this challenge, a 1-2-3-5-7... sequence is an ...
- 1,735
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13
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+200
Output a 1-2-3 sequence
For the purposes of this challenge, a 1-2-3 sequence is an infinite sequence of increasing positive integers such that for any positive integer \$n\$, exactly one of \$n, 2n,\$ and \$3n\$ appears in ...
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votes
4
answers
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Draw a Fibonacci Swoosh
Title courtesy of Greg Martin
For this challenge, I'll define an arc of size \$k\$ as a single piece of a sine wave with a length of \$k\$ units and an height of \$\frac{k}{4}\$ units:
And I'll ...
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6
votes
12
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Argument of a complex number (Robbers)
V1.1: Added criterion to help with tiebreakers, a bit overkill but still.V1.2: It's April 15th!
Task: Crack the scrambled code for calculating the argument of a complex number \$z=x+iy\$ given two ...
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Argument of a complex number (Cops)
This is the cop's thread, where one should post the scrambled code. Here is the robbers' thread where the cracked source should be posted and linked to the cop's answer.
NB: I am currently writing up ...
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7
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How quickly can you type this unary string?
If I want to type the string aaa, the least keystrokes I can type it in is 3: a a a. But if I want to type the string ...
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7
votes
2
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Convert maximum values to bit widths
Background
The newest version of the C standard, C23, adds preprocessor macros like INT_WIDTH, ULONG_WIDTH, and ...
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12
votes
14
answers
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Lattice points visible from the origin
Challenge
Create a program that outputs a square grid showing visible and non-visible points \$(x, y)\$ from the origin based on their greatest common divisor (GCD).
A point \$(x, y)\$ is considered ...
- 2,163
18
votes
26
answers
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Is it a tetrate of two?
The tetration operation consists of repeated exponentiation, and it is written ↑↑. For instance,
3↑↑3 =3 ^(3^3) = 3^27 = 7,625,597,484,987
A tetrate of two is an ...
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12
votes
6
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Contract a tensor
Introduction
Tensor contraction is an operation that can be performed on a tensor. It is a generalization of the idea of the trace of a matrix. For example, if we have a rank-2 tensor (a matrix) and ...
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Egyptian fraction representations of 1 without prime denominators
Background
As noted in this question, for all positive integers \$n>2\$ there exists at least one Egyptian fraction representation (EFR) of \$n\$ distinct positive integers \$a_{1} < a_{2} < \...
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votes
12
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810
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Sum up snail number neighbours
Input: You are given two numbers n and m.
Create the snail: Given an n >= 3, fill an <...
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14
votes
13
answers
1k
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Counting rankings
There is a competition with \$n\$ participants in total. Alice is one of the participants. The outcome of the competition is given as a ranking per participant with a possibility of ties; e.g. there ...
- 76k
3
votes
4
answers
639
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Fastest count of certain hypercubes with labeled vertices
CHALLENGE
This is a fastest-code challenge.
Count how many n-dimensional hypercubes with n=1,2,3,4 exist, with vertices labeled with either 1 or 0, such that there does not exist any rectangle formed ...
- 139
4
votes
5
answers
390
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Generate a sequence of \$n\$ consecutive composite numbers
Definitions
The common methods to generate consecutive composites are
$$\overbrace{(n+1)! + 2, \ (n+1)! + 3, \ \ldots, \ (n+1)! + (n+1)}^{\text{n composites}}$$
$$\overbrace{n!+2,n!+3,...,n!+n}^{\text{...
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vote
8
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Alternating Random Series Sum To \$N\$ [closed]
Challenge
Given a positive integer \$N \ge 3\$, generate an alternating series of \$N\$ random numbers within the range \$[1, N]\$, such that their sum equals \$N\$. Expressed mathematically as
$$N = ...
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votes
8
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Number of cigarettes that can be made from a given number of butts
Assumption
A cigarette can be made by combining four cigarette butts. Cigarette butts last infinitely until smoked.
Explanation
Say you have 31 butts. That means, you can make 7 cigarettes from 28 ...
12
votes
20
answers
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Modular Equivalence
Given two numbers \$x,y > 2, x≠y \$ output all integers \$m\$ such that
$$
x + y \equiv x \cdot y \pmod m
$$
$$
x \cdot y > m > 2
$$
Input
Two integers
Output
A list of integers
Test cases
<...
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votes
19
answers
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The TAK function (easy mode)
The TAK function is defined as follows for integers \$x\$, \$y\$, \$z\$:
$$
t(x, y, z) = \begin{cases}
y, & \text{if $x \le y$} \\
t(t(x-1,y,z), t(y-1,z,x), t(z-1,x,y)), & \text{otherwise}
\...
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The TAK function
The TAK function is defined as follows for integers \$x\$, \$y\$, \$z\$:
$$
t(x, y, z) = \begin{cases}
y, & \text{if $x \le y$} \\
t(t(x-1,y,z), t(y-1,z,x), t(z-1,x,y)), & \text{otherwise}
\...
- 76k
13
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20
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Complete a Mystery Sequence
Given a sequence of three integers, determine if the sequence is arithmetic (of the form [a, a+d, a+2*d]) or geometric (of the form ...
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votes
10
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960
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Make 1's and 2's composite
Input
An integer k composed of 1 and 2, with at least 3 digits and at most 200 digits.
...
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25
answers
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Consecutive Composite Numbers
Challenge
Generate \$n-1\$ consecutive composite numbers using this prime gap formula
$$n!+2,n!+3,...,n!+n$$
Input
An integer \$n\$ such that \$3 \leq n \leq 50 \$.
Output
Sequence of \$n-1\$ ...
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17
votes
19
answers
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Ellipse Lattice Point Counter
Challenge
Determine how many integer lattice points there are in an ellipse
$$\frac{x^2}{a^2} + \frac{y^2}{b^2} \leq 1$$
centered at the origin with width \$2a\$ and height \$2b\$ where integers \$a, ...
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-6
votes
1
answer
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Where to stand to throw circles over sticks
Consider a horizontal line with vertical lines centered on the x-axis and placed at gaps of \$\sqrt{2}/2\$. For a positive integer \$n \geq 3\$, the first half of the lines have lengths \$0, \sqrt{2},...
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15
votes
21
answers
2k
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Divmod continuously until the remainder is 1 or 0, then get the remainder
The task is simple, divide, get the quotient and the remainder, and if the remainder isn't 1 or 0, do the same thing (quotient divmod remainder) until the remainder is 1 or 0, then get the remainder. ...
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Counting Collinear Points
Given two points \$(x_1, y_1)\$ and \$(x_2, y_2)\$ with integer coordinates, calculate the number of integer points (excluding the given points) that lie on the straight line segment joining these two ...
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Find the optimum circle in an infinite grid
Consider an \$n \times n\$ grid of integers which is part of an infinite grid. The top left coordinate of the \$n \times n\$ grid of integers is \$(0, 0)\$.
The task is to find a circle which when ...
- 2,896
11
votes
20
answers
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Calculate 500 digits of e
Write a program to calculate the first 500 digits of the mathematical constant e, meeting the rules below:
It cannot include "e", "math.e" or similar e constants, nor may it call ...
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9
votes
3
answers
474
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Coin sequence probability
Given two strings containing only 0 and 1, decide the probability that first appears earlier as a consecutive substring in an ...
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16
votes
2
answers
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Construct this point
Given a constructible point \$(x, y) \in \mathbb R^2\$, output the steps required to construct \$(x, y)\$
Constructing a point
Consider the following "construction" of a point \$(\alpha, \...
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19
votes
9
answers
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Output an infinitely proportional sequence
In this challenge, an infinitely proportional sequence is defined as a infinite sequence of positive integers such that:
All positive integers are contained infinitely many times within the sequence.
...
- 37.8k
7
votes
3
answers
194
views
Inscribe a maximal regular polygon into a square image
You want to draw a regular polygon but you have limited space! In this challenge, you should draw a polygon with n sides which is as big as possible for a given square container image.
I found ...
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18
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24
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Test whether a sequence is bitonic
You know what a monotonic sequence is: each element is bigger than its predecessor (monotonically rising) or as its successor (monotonically falling).
Bitonic means you have two arms of the sequence, ...
- 2,501
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7
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Auto-golf an esolang
The lack of a social life drove a poor nerd into inventing another superfluous esolang called !+~%. For no good reason it initializes the accumulator with ...
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votes
11
answers
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Print 100 digits of Champernowne's Constant
Inspired by this and this question
Challenge
Your challenge is to print any 100 consecutive digits of Champernowne's Constant. You must give the index at which that subsequence appears. The 0 at the ...
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votes
17
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What's the character limit of this text field? [duplicate]
Someone I know has no coding experience, but has proposed an algorithm* to determine the character limit of text fields they find online. They copy a string containing the numbers from 1 to 1,000 ...
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7
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Night hike partitioning
We want to go on a night hike with the youth group, but of course not everyone has their torch, even though we told them we planned to split up. What options are there for group formation if n teens ...
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16
votes
16
answers
4k
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Which skill to train?
Story (skip, if you prefer the naked task): You need five skills for an imaginary sport: Speed, strength, endurance, accuracy and tactics. If you achieve a score in each of these disciplines, you can ...
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4
votes
1
answer
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Convert real numbers between factoradic and positive integer bases
This prompt asked you to convert back and forth to factoradic, but is very limited in scope (only decimal integers from 0 to 10!-1). Your task in this challenge is to reach just a bit further and ...
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Produce a secure block cipher round function (1 bit round key; 7 bit message)
We need to produce a block cipher round function with a 1 bit round key size and a 7 bit message size with the highest level of cryptographic security according to our measure of security.
...
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votes
8
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Produce the shortest suffix for an (almost) arbitrary string
I encountered some silly code from a game and I figured this would actually turn into a fun golfing problem, so:
Given any ASCII string in the limited char range specified below.
Append as few ...
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6
answers
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Sine using square root [closed]
Given input \$x \in \left\{0,3,6,...,90\right\}\$, output \$\sin\left(x°\right)\$ using integer and \$+ - \times \div ( ) \sqrt{\cdot}\$(square root), e.g. \$\sin(45°)=\sqrt{1\div 2}\$.
Flexible ...
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17
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14
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Finding the power sandwich version 2
Introduction
This question is inspired by this great question.
Challenge
Given a number \$N>0\$, output the largest integer \$a^b\$ that is smaller or equal to \$N\$, and the smallest integer \$c^d\...
15
votes
16
answers
2k
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Finding the power sandwich
Introduction
Finding the closest power to a number is a common enough problem. But what if you need both the next-highest and next-lowest power? In this challenge you must find the closest powers to a ...
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votes
6
answers
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Hermite interpolation
We already have a challenge for polynomial interpolation: given a list of points, output the coefficients of the polynomial that passes through them.
Hermite interpolation is a generalization of ...
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Expected number of rounds for this labeling scheme
Task
Here is an interesting math problem:
Let's say that there are \$n\$ indistinguishable unlabeled objects in a bin. For every "round", pull \$k\$ objects randomly out of the bin with ...
- 13.3k
9
votes
5
answers
524
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Write a variadic fixed point combinator
A fixed-point combinator is a higher order function \$\mathrm{fix}\$ that returns the fixed point of its argument function. If the function \$f\$ has one or more fixed points, then $$\mathrm{fix} f=f(\...
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votes
2
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Visualise the Euclidean GCD [duplicate]
The Euclidean GCD Algorithm is an algorithm that efficiently computes the GCD of two positive integers, by repeatedly subtracting the smaller number from the larger number until they become equal. It ...
- 37.8k
16
votes
18
answers
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Divisor chain counts (1 3 3 7 ...)
The divisors of a natural number form a poset under the relation of "a divides b?", \$a | b\$. This challenge is to produce the number, \$C\$, of non-empty chains of such posets for natural ...
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