Questions tagged [math]
The challenge involves mathematics in some central way. Also consider using more specific tags, listed in the tag wiki info.
1,683
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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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Bridges of Königsberg [closed]
This is a famous mathematical problem, Named as Bridges of Königsberg
Task
The bridges of Königsberg is a problem in mathematics which states that the path required for crossing each bridge exactly ...
5
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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 ...
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5
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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 ...
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10
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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) ...
- 96.3k
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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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Length of Binary as Base 10 [OEIS A242347]
Computers like binary. Humans like base 10. Assuming users are humans, why not find the best of both worlds?
Your task is to find the first n terms in the sequence ...
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Generate the n'th Fermi-Dirac Prime
A Fermi-Dirac Prime is a prime power of the form \$p^{2^k}\$, where \$p\$ is prime and \$k \geq 0\$, or in other words, a prime to the power of an integer power of two. They are listed as integer ...
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14
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Minimum rotation to get the maximum value
I recently solved a coding challenge in one of the challenge papers that my IT teacher gave to us. It was a seemingly simple, but fun challenge, so I thought it will make fun golfing.
The task
Given ...
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Triangular honeycomb numbers
From the infinite triangular array of positive integers, suppose we repeatedly select all numbers at Euclidean distance of \$\sqrt{3}\$, starting from 1:
$$
\underline{1} \\
\;2\; \quad \;3\; \\
\;4\; ...
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Triangular polkadot numbers
From the infinite triangular array of positive integers, suppose we select every 2nd numbers on every 2nd row as shown below:
$$
\underline{1} \\
\;2\; \quad \;3\; \\
\;\underline{4}\; \quad \;5\; \...
- 67.9k
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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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Prime number checksum
Given a message, append checksum digits using prime numbers as weights.
A checksum digit is used as an error-detection method.
Take, for instance, the error-detection method of the EAN-13 code:
The ...
- 5,421
4
votes
2
answers
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Partial Fractions
Given an input of a string, output the partial fraction in string form.
The partial fraction decomposition of a rational fraction of the form \$\frac{f(x)}{g(x)}\$, where \$f\$ and \$g\$ are ...
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A decimal-based unit of time
Background
In 1960, the 11th General Conference on Weights and Measures defined the Système International d'Unités (SI) Units which scientists still use today.
The metre and the kilogram became ...
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It's Just Rocket Science, Part 2 - Centrifuge
You've gotten out of Earth's gravity well - good for you! However, you're feeling a bit uncomfortable in zero-gravity, and you want to replicate 1 \$g\$ of force in a centrifuge. Use the equation for ...
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Count Futoshiki row solutions
Futoshiki is a logic puzzle where an \$n×n\$ Latin square must be completed based on given numbers and inequalities between adjacent cells. Each row and column must contain exactly one of each number ...
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Find The Real Solutions of a Cubic
Description
All cubic equations can be solved, and every cubic has at least one solution. The goal of this challenge is to find the real solutions to a given cubic using inputs, and (obviously) the ...
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It's Just Rocket Science
Write a program/function that finds the amount of fuel needed to escape Earth's gravity well given the exhaust velocity of the fuel and the amount of mass to transport using the Tsiolkovsky rocket ...
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Carryless factors
Carryless multiplication is an operation similar to binary long multiplication, but with XOR instead of addition:
...
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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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13
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Reconstruct Matrix from its diagonals
Given the diagonals of a matrix, reconstruct the original matrix.
The diagonals parallel to the major diagonal (the main diagonals) will be given.
Diagonals: ...
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Compute the Fabius Function
The Fabius function is an example of a function that is infinitely differentiable everywhere, yet nowhere analytic.
One way to define the function is in terms of an infinite number of random variables....
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Calculate Pi unto a point using the Nilakantha series
Your task: given a nonzero positive number i, calculate pi using the Nilakantha series unto i terms.
The Nilakantha series is as ...
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5
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Detect round trips on a dodecahedron
An ant starts on an edge of a dodecahedron, facing parallel to it. At each step, it walks forward to the next vertex and turns either left or right to continue onto one of the other two edges that ...
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The second even sublime number
easy mode of my previous challenge
A perfect number is a positive integer whose sum of divisors (except itself) is equal to itself. E.g. 6 (1 + 2 + 3 = 6) and 28 (1 + 2 + 4 + 7 + 14 = 28) are perfect.
...
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An algorithm to find even sublime numbers
A perfect number is a positive integer whose sum of divisors (except itself) is equal to itself. E.g. 6 (1 + 2 + 3 = 6) and 28 (1 + 2 + 4 + 7 + 14 = 28) are perfect.
A sublime number (OEIS A081357) is ...
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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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Cartesian - polar conversion couple
We don't have a challenge for conversion between Cartesian and polar coordinates, so ...
The challenge
Write two programs (or functions) in the same language:
one that converts from polar to ...
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Anti-divisors of a number
Given a positive integer n, output all of its anti-divisors in any order.
From OEIS A006272:
Anti-divisors are the numbers that do not divide a number by the ...
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28
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Triangle area from side lengths
Output the area \$A\$ of a triangle given its side lengths \$a, b, c\$ as inputs. This can be computed using Heron's formula:
$$ A=\sqrt{s(s-a)(s-b)(s-c)}\textrm{, where } s=\frac{a+b+c}{2}.$$
This ...
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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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Squash it ... again!
If you place the positive integers together and read each set of two adjacent digits at the same time, you get: (A136414)
...
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Implement pow with overflow checking
Implement a function or program which raises x to the power of y. Inputs are 16-bit signed integers. That is, both are in the ...
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Implement Binary Exponentiation
Background
In programming, there is a recursive algorithm called binary exponentiation, which allows for large integer powers to be calculated in a faster way. Given a non-zero base \$x\$ and a non-...
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Weighted coin flip strings
Given n, k, and p, find the probability that a weighted coin with probability p of heads will flip heads at least k times in a row in n flips, correct to 3 decimal digits after decimal point (changed ...
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Not-Roman-Numeral Addition
Write the shortest program or function that mimics the addition in this XKCD strip:
Input
Two positive decimal integers containing only the digits 150.
Output
The ...
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10
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Divide by an odd number, 2-adically
Given \$a\$ and \$b\$, both odd \$n+1\$-bit integers, compute \$a/b\$ to a precision of \$n+1\$ bits in the 2-adic integers. That is, compute \$c\$ such that \$a = bc\, (\mathop{\rm mod} 2^{n+1})\$. \$...
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Print the power set of the power set ... of an empty set
Given a non-negative integer n, print the result of P(P(...P({}))), where the number of P's ...
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Calculate the Lowest Even-Harmonic of the Values in a List
PROBLEM
For a list of numbers, list: Find the lowest possible integer, x, which is optimally close to the whole number even-...
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Divisible subset sums
Inspired by the recent 3Blue1Brown video
Consider, for some positive integer \$n\$, the set \$\{1, 2, ..., n\}\$ and its subsets. For example, for \$n = 3\$, we have
$$\emptyset, \{1\}, \{2\}, \{3\}, \...
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In between fractions
Given two positive integer fractions \$x\$ and \$y\$ such that \$x < y\$, give the fraction \$z\$ with the smallest positive integer denominator such that it is between \$x\$ and \$y\$.
For example ...
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Alternating sums of multidimensional arrays
Given a multidimensional array, find the recursive alternating sum. An alternating sum is simply the sum of an array, where every other item (starting with the second) is negated. For example, the ...
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ASCII-Art n'th Root
Challenge:
Given two integers \$a\$ and \$b\$, with lengths \$A=length(a), B=length(b)\$, output an ASCII-art of the \$a^{th}\$ root of \$b\$, including the answer rounded to \$A\$ amount of decimal ...
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Best performance on x/(y+z) + y/(x+z) + z/(x+y) = N
Consider the equation $$\frac x {y+z} + \frac y {x+z} + \frac z {x+y} = n$$ for positive integers \$x, y, z\$ and \$n \ge 4\$. Your code will receive \$n\$ as an input, and output three integers \$x, ...
- 1,474
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Sorting passengers on a plane
A few days ago I made a puzzle about moving people on an airplane. Now I am interested in the general version of this puzzle and the shortest code golf for it.
I will briefly summarise the puzzle here....
