Questions tagged [math]
The challenge involves mathematics in some central way. Also consider using more specific tags, listed in the tag wiki info.
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Funny Numbers :D
The task is to calculate the average "funniness" of a given number given the following scoring system:
1 point for each "420" in it
2 points for each "69" in it
3 points ...
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Raise integer x to power x, without exponentiation built-ins
Task - The title pretty much sums it up: raise an integer x to power x, where 0<x.
Restrictions:
Use of exponentiation, ...
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Last digit large number
For a given list of number \$[x_1, x_2, x_3, ..., x_n]\$ find the last digit of \$x_1 ^{x_2 ^ {x_3 ^ {\dots ^ {x_n}}}}\$
Example:
...
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How many ways to cut a number into an equation?
Too bad! I had such a beautiful equation, but I lost all my =+-*, so there is nothing left but a chain of digits, looking like a number: ...
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Find the smallest integer multiple of a Decimal
The Challenge
Given a rational number, determine the smallest number which is a positive integer multiple of it. Eg.
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Generate a Kirkman triple system
Given a universe of \$v\$ elements, a Kirkman triple system is a set of \$(v-1)/2\$ classes each having \$v/3\$ blocks each having three elements, so that
every pair of elements appears in exactly ...
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Find a number which generates all the integers mod q
Consider the integers modulo q where q is prime, a generator is any integer 1 < x < q ...
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Sums of sum of divisors in sublinear time
Given a number \$n\$, we have its sum of divisors, \$\sigma(n)\ = \sum_{d | n} {d}\$, that is, the sum of all numbers which divide \$n\$ (including \$1\$ and \$n\$). For example, \$\sigma(28) = 1 + 2 +...
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What's my score?
The question score on Stack Exchange is the total number of upvotes minus the total number of downvotes a question receives. However, the reputation gained/lost for every upvote/downvote is different (...
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Find the number in the Champernowne constant
Introduction
In base 10, the Champernowne constant is defined by concatenating representations of successive integers. In base 10: 0.1234567891011121314151617... ...
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American odds to probabilities
American odds (aka moneyline odds) are numbers like \$+150\$ or \$-400\$ used to express how much a winning bet would pay out. Convert odds to a fair win probability like this:
Positive odds \$+n\$ ...
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Sums of Euler's totient function in sublinear time
Related.
Given a number \$n\$, Euler's totient function, \$\varphi(n)\$ is the number of integers up to \$n\$ which are coprime to \$n\$. That is, no number bigger than \$1\$ divides both of them.
For ...
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Print, Increment, Decrement, Alias - Interpret Prindeal
Prindeal (pronounced prin-dee-al) is a new esoteric programming language that only has four commands: print, increment, decrement, and alias. Despite its minimalism, complex mathematical operations ...
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Minimum excluded number
This is intended to be an easy, bite-size code-golf.
The mex (minimal excluded number) of a finite collection of numbers is the smallest non-negative integer ...
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count ones in range
Challenge :
Count the number of ones 1 in the binary representation of all number between a range.
Input :
Two non-decimal positive integers
Output :
The sum of ...
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Ryley's Theorem
S. Ryley proved following theorem in 1825:
Every rational number can be expressed as a sum of three rational cubes.
Challenge
Given some rational number \$r \in \mathbb Q \$ find three rational ...
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The Rien Number
The Champernowne constant is a number that is constructed by concatenating the first n numbers, with n tending to infinity. It ...
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XOR multiplication
You goal is to implement the operation of XOR (carryless) multiplication, defined below, in as few bytes as possible.
If we think of bitwise XOR (^) as binary ...
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Add two really big numbers
Preamble
We've already proven we're good at adding two numbers, but many solutions only operate on tiny numbers like 2³²-1, honestly we can do a lot better.
The Challenge
Given two unsigned, non-...
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Greatest Common Divisor
Your task is to compute the greatest common divisor (GCD) of two given integers in as few bytes of code as possible.
You may write a program or function, taking input and returning output via any of ...
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Find the perfect square!
Your task is to turn a square root like this:
√12
into a form like this:
2√3
For our purpose, we only need to output the left ...
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Sum of consecutive nth powers
Related.
Given a positive integer \$n\$, output all integers \$b\$ (such that \$1<b<n-1\$) where \$n\$ can be written as the sum of any number of consecutive powers of \$b\$.
Example:
Let's say \...
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Write a microwave timer!
You are an employee of Microteque, a leading Silicon Valley startup creating smart microwave ovens for all kinds of strange places. Your customers can get their microwaves printed with patterns to ...
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Decimalize a Fraction
Preamble
A common pain-point when working with rational numbers and decimals is how infrequently one can represent their rational number as a clean, non-repeating decimal. Let's solve this by writing ...
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Euler-Poincaré-Characteristic of Polyhedra
Given a triangulation of the surface of a polyhedron p, calculate its Euler-Poincaré-Characteristic χ(p) = V-E+F, where ...
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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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Calculate Power Series Coefficients
Given a polynomial \$p(x)\$ with integral coefficients and a constant term of \$p(0) = \pm 1\$, and a non-negative integer \$N\$, return the \$N\$-th coefficient of the power series (sometimes called &...
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Programming Languages Through The Years
In this challenge, users will take turns completeing three fairly simple coding tasks in programming languages that are allowed to be progressively older.
The first answer must use a programming ...
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The Ackermann function
The Ackermann function is notable for being the one of the simplest examples of a total, computable function that isn't primitive recursive.
We will use the definition of \$A(m,n)\$ taking in two ...
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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\$ ...
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Prime polynomials
Given a polynomial, determine whether it's prime.
A polynomial is ax^n + bx^(n-1) + ... + dx^3 + ex^2 + fx + g, where each term is a constant number (the ...
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Polynomialception
Given two polynomials f,g of arbitrary degree over the integers, your program/function should evaluate the first polynomial in the second polynomial. ...
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Self Referential Polynomials
For every given degree \$n\$ it is possible to construct (at least one) an integral polynomial \$p \in \mathbb Z[X]\$ such that \$p(k)\$ (\$p\$ evaluated in \$k\$) is the coefficient of the term \$x^k\...
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Vanilla Natural Logarithm Challenge
There is a challenge for multiplying two numbers so I guess this counts too
Given as input a positive real number n compute its natural logarithm.
Your answer ...
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Is this polynomial a square?
Given an integral polynomial \$p\$, determine if \$p\$ is a square of another integral polynomial.
An integral polynomial is a polynomial with only integers as coefficients.
For example, \$x^2+2x+1\$ ...
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Is it a factor of a polynomial?
A polynomial is divisible by a factor (x-n) if f(n)=0 for a function f. Your job: to ...
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Calculate the Distance to a Line Segment
The Challenge
Given two vertexes and a point calculate the distance to the line segment defined by those points.
This can be calculated with the following psudocode
...
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Matrix Trigonometry
Introduction
The two most common trigonometric functions, sine and cosine (or sin and ...
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Product over a range
Your task is simple: given two integers \$a\$ and \$b\$, output \$\Pi[a,b]\$; that is, the product of the range between \$a\$ and \$b\$. You may take \$a\$ and \$b\$ in any reasonable format, whether ...
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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
...
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Characteristic polynomial
The characteristic polynomial of a square matrix \$A\$ is defined as the polynomial \$p_A(x) = \det(Ix-A)\$ where \$I\$ is the identity matrix and \$\det\$ the determinant. Note that this definition ...
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Construct the Identity Matrix
The challenge is very simple. Given an integer input n, output the n x n identity matrix. The identity matrix is one that has <...
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11
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Olympic game scoring [closed]
The challenge is to write a golf-code program that, given n positive real numbers from 0 to 10 (format x.y, y only can be 0 or 5: 0, 0.5, 1, 1.5, 2, 2.5 … 9.5 and 10), discard the lowest and highest ...
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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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Exponential transform of an integer sequence
The exponential generating function (e.g.f.) of a sequence \$a_n\$ is defined as the formal power series \$f(x) = \sum_{n=0}^{\infty} \frac{a_n}{n!} x^n\$.
When \$a_0 = 0\$, we can apply the ...
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Multiplicity of a root of a polynomial
Let \$p(x)\$ be a polynomial. We say \$a\$ is a root of multiplicity \$k\$ of \$p(x)\$, if there is another polynomial \$s(x)\$ such that \$p(x)=s(x)(x-a)^k\$ and \$s(a)\ne0\$.
For example, the ...
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Output the Juggler sequence
The Juggler sequence is described as follows. Beginning with an input \$a_1\$, the next term is defined by the recurrence relation
$$a_{k+1} = \begin{cases}
\left\lfloor a_k ^ \frac 1 2 \right\rfloor,\...
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Cutting a Circular Pizza Vertically
Most people would cut circular pizzas into circular sectors to divide them up evenly, but it's also possible to divide them evenly by cutting them vertically like so, where each piece has the same ...
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Is this set laminar?
A family of sets is called laminar if for any two sets \$A\$ and \$B\$ in the family one of the following is true:
\$ A \subseteq B \$
\$ A \supseteq B \$
\$ A \cap B = \emptyset \$
Or less ...
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Leyland Numbers
Given a natural number \$n\$, return the \$n\$-th Leyland number.
Leyland Number
Leyland numbers are positive integers \$k\$ of the form
$$k = x^y + y^x$$
Where \$x\$ and \$y\$ are integers strictly ...
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