Questions tagged [math]
The challenge involves mathematics in some central way. Also consider using more specific tags, listed in the tag wiki info.
1,727
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Output endless powers of 2 [duplicate]
In any programming language, make a program that outputs infinite subsequent powers of two, starting at any power of two with finite integer exponent. There does not need to be a seperator between ...
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Logarithmic Incrementation
In this challenge you will write a function that takes a list (ordered set) containing real numbers (except for the empty list) and calculates
$$f(x)=\begin{cases}1 & \text{if } |x|=0 \\ x_1+1 &...
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How many sorting networks?
Below on the left is a picture of a sorting network that can sort 4 inputs. On the right you can see it sorting the input 3,2,4,1.
A sorting network of size ...
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Resultant of two polynomials
The resultant of two polynomials is a polynomial in their coefficients that is zero if and only if \$p\$ and \$q\$ have a common root. It is a useful tool for eliminating variables from systems of ...
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Euclidean distance on projective plane
Motivated by this challenge
Background
Let we have a square sheet of flexible material.
Roughly speaking, we may close it on itself four ways:
Here the color marks the edges that connect and the ...
- 3,031
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How powerful must this e approximation be?
This challenge was inspired by this non-challenge about the natural logarithm base \$e\$ and the following pandigital approximation to \$e\$ appearing on a Math Magic page:
$$\left|(1+9^{-4^{7×6}})^{3^...
- 3,637
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Representing a number as an unordered list of smaller numbers
Suppose we want to encode a large integer \$x\$ as a list of words in such a way that the decoder can recover \$x\$ regardless of the order in which the words are received. Using lists of length \$k\$ ...
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Compare Two Fractions With ASCII Art
Challenge
Write a program or function that takes in 4 non-negative integers, A, B, C, and D, that represent two fractions, A/B and C/D, where B and D are non-zero and A <= B and C <= D.
Output ...
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Minkowski's ?(x) for rational x
Here is Minkowski's question mark function:
It is a strictly increasing and continuous function from the reals to themselves that, among other unusual properties, maps rational numbers to dyadic ...
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Calculate the Smith normal form of an integer matrix
Given an \$m \times n\$ matrix of integers A, there exist a \$m \times m\$ matrix P, an \$m \times n\$ matrix D, and an \$n \times n\$ matrix Q such that:
\$A = P D Q\$.
P and Q are unimodular ...
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Calculate Euclidean distance on a torus
Euclidean distance between two lattice points \$(x_1, y_1)\$ and \$(x_2, y_2)\$ on a plane is: \$\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\$.
Imagine now a lattice ...
- 13.1k
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Find Index of Rational Number in Calkin-Wilf Sequence
Related
From Wikipedia:
In number theory, the Calkin–Wilf tree is a tree in which the vertices correspond one-to-one to the positive rational numbers. The tree is rooted at the number \$1\$, and any ...
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Hankel transform of an integer sequence
A Hankel matrix is a square matrix in which each ascending skew-diagonal from left to right is constant, e.g.:
$$\begin{bmatrix} a & b & c & d \\ b & c & d & e \\ c & d &...
- 41.9k
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Add two real numbers ... probably
The problem statement here is pretty simple, take two real numbers on the range [0,1) as input and output their sum, with probability 1.
The catch here is that there are a lot of real numbers. There ...
- 94.5k
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Alternating factorial
The alternating factorial is an alternating sum of decreasing factorials. For example, we could calculate the alternating factorial of 4 as follows:
First, calculate the factorials from 4 down to 1:
...
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The Jaccard Index
The Jaccard index / similarity coefficient, also known as the Tanimoto index / coefficient, is a statistic used for gauging the similarity and diversity of finite sample sets. It was developed by ...
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Cosine similarity of two vectors
The cosine similarity of two vectors \$A\$ and \$B\$ is defined using their dot product and magnitude as:
\$\frac{A\cdot B}{\|A\|\|B\|}\$
Or in other terms
\$\frac{\sum_{i=1}^nA_iB_i}{\sqrt{\sum_{i=1}^...
- 1,696
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Enumeration of free polyominoes
A polyomino with \$n\$ cells is a shape consisting of \$n\$ equal squares connected edge to edge.
No free polyomino is the rotation, translation or reflection (or a combination of these ...
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Record Least Uncommon Multiple Counts
The Greatest Common Divisor, or gcd, of two positive integers \$x\$ and \$y\$ is the largest positive integer that divides both \$x\$ and \$y\$.
The Least Common Multiple, or lcm, of two positive ...
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We're gonna need a bigger podium!
If \$R\$ runners were to run a race, in how many orders could they finish such that exactly \$T\$ runners tie?
Challenge
Given a positive integer \$R\$ and a non-negative integer \$0\leq T\leq {R}\$ ...
- 99.7k
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Detect round trips on a hyperbolic grid
You're driving a car in an infinite city whose blocks are pentagons arranged in the order-4 pentagonal tiling. At each step, you proceed to the next intersection and choose whether to continue left, ...
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Classify a surface from its fundamental polygon
This question is an extension of Who's that Polygon? to arbitrary numbers of sides.
A fundamental polygon for a surface is an polygon with a prescribed pairing for all its \$2n\$ sides, each ...
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Generate all possible equations with 10 characters
Nerdle is a Wordle variant, in which instead of words, the answers are equations. Each equation entered in the game must be a valid one.
Examples: 13³-1=2196, ...
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Canonical form of a cubic Bézier curve
On Pomax's Primer on Bézier Curves this "fairly funky image" appears:
This is related to the fact that every cubic Bézier curve can be put in a "canonical form" by an affine ...
- 3,637
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4D rotation matrix to quaternions
It is well-known that a 3D rotation can always be represented by a quaternion. It is less well-known that a 4D rotation can always be represented by two quaternions, sending a point \$p=(a,b,c,d)^T\$ ...
- 3,637
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Number Clusters
Your task is to create a program or function, that when given an input list of nonnegative integers of length \$l \ge 2\$ and a nonnegative integer \$c\$ where \$2 \le c \le l\$, group the list into \$...
- 3,100
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votes
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3D rotation matrix to quaternion
There are multiple ways to represent a 3D rotation. The most intuitive way is the rotation matrix –
$$A=\begin{bmatrix}A_{11}&A_{12}&A_{13}\\A_{21}&A_{22}&A_{23}\\A_{31}&A_{32}&...
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Split some points
proposed by @Adám in chat
Given an even number of finite points return a line \$y=mx+b\$ that evenly splits the points on both sides.
Specs
Take a list of distinct points \$(x,y)\$ (or a list of x-...
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How spherical is my ellipsoid?
Define the (unnormalised) Willmore energy of a surface as the integral of squared mean curvature over it:
$$W=\int_SH^2\,dA$$
For surfaces topologically equivalent to a sphere \$W\ge4\pi\$, and \$W=4\...
- 3,637
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Ptolemy's table of chords
Ptolemy's Almagest contains a table of chords that effectively served as the world's only comprehensive trigonometric table for over a millennium. In modern form it looks like this:
\begin{array}{|l|...
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Time to shortest permutation
Yesterday, as part of a IQ-style test, I got this interesting question:
The time on a 24-hour clock is 11:43. What is the least number of minutes I should wait before the same digits are on the ...
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Sum of Consecutive Squares
Your task
Given a integer input, \$ n \$ (such that \$ n > 1 \$), decide whether it can be written as the sum of (at least 2) consecutive square numbers.
Test cases
Truthy:
...
- 11.5k
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Capture the Flag... with a twist
Inspired by a challenge from the OUCC 2022 Seniors competition.
Background
Two teams are playing "capture the flag". They take turns invading each other's base and capturing their opposing ...
- 11.5k
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Intersection area of two rotated rectangles
Given two rectangles, which are possibly not in the orthogonal direction, find the area of their intersection.
Input
You may take the rectangles as input in one of the following ways:
The ...
- 41.9k
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Round to nicer numbers
The standard way to round numbers is to choose the nearest whole value, if the initial value is exactly halfway between two values, i.e. there is a tie, then you choose the larger one.
However where I ...
- 94.5k
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Maximum of outer product of integer vectors (in linear time)
Introduction
Our goal is to efficiently find the maximum of a large amount of (redundant) data.
We define the outer product of vectors \$A\$ and \$B\$ as a matrix containing the products of all ...
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RADD decomposition of an integer
Introduction
The \$RADD(n)\$ operation is defined as the sum of \$n + [\$ the number whose decimal representation are the decimal digits of \$n\$ in reverse order \$]\$, see A004086. After reversal, ...
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Implement the Riemann R function
The Riemann R function is as follows:
$$R (x)=\sum _{n=1}^{\infty } \frac{\mu (n) \text{li}\left(x^{1/n}\right)}{n}.$$
This uses the Möbius function as well as the logarithmic integral.
From Wikipedia,...
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Normal Subgroups of \$S_4\$
Objective
Given a permutation of 4 distinct items, classify the permutation by the normal subgroup(s) it belongs.
Input/Output Format
You gotta choose the followings as the hyperparameters for your ...
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Calculate my income tax
Background
Here in the UK1, these are the income tax rules:
You get a personal allowance (untaxed) of up to £12,570:
If you earn less than £100,000, you get the full £12,570 as personal allowance
...
- 11.5k
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Sum every second digit in a number
I have a number like this:
n = 548915381
The output should be the sum of every second number. In this case 26:
4+9+5+8 = 26
...
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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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Output the length of (the length plus a message) [duplicate]
The task is simple. You're given an arbitrary string message. Return that message prefixed with a number, such that the length of that number plus the message equals the number. In other words, the ...
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CGAC2022 Day 3: \$n\$-dimensional Chocolate Pyramid
Part of Code Golf Advent Calendar 2022 event. See the linked meta post for details.
I've got an infinite supply of \$n\$-dimensional chocolate for some positive integer \$n\$. The shape of the ...
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CGAC2022 Day 1: Let's build a chocolate pyramid!
Following last year's event, we're doing Code Golf Advent Calendar 2022!
On each day from today (Dec 1) until Christmas (Dec 25), a Christmas-themed challenge will be posted, just like an Advent ...
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Transform a lattice polygon to minimum diameter by shearing
Given is a grid polygon by the list of its integer vertex coordinates arranged along the perimeter, in the form
\$(x_1,y_1), (x_2,y_2), \cdots , (x_n,y_n)\$ with \$n \ge 3\$.
The polygon is completed ...
- 701
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Perfect Nontransitive Sets
Background
For the purposes of this challenge, we'll define a "perfect nontransitive set" to be a set \$A\$ with some irreflexive, antisymmetric relation \$<\$, such that for all \$a \in ...
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Maximum average ord
Your task
Take a list of strings as the input, and output the maximum average ord.
Example
Given the list ...
- 11.5k
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Counting Stripey Bracelets
A bracelet consists of a number, \$\mathit{N}\$, of beads connected in a loop. Each bead may be any of \$\mathit{C}\$ colours. Bracelets are invariant under rotation (shifting beads around the loop) ...
- 99.7k
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Power sequence differences
Your task
Given two positive integers \$x\$ and \$d\$ (such that \$d<x\$), output the 5th term of the \$d\$th difference of the sequence \$n^x\$
Example
Let's say we are given the inputs \$x=4\$ ...
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