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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Sample space of n consecutive coin flips [duplicate]

Taking a positive integer n as input, print the sample space of n consecutive coin flips. The coin is fair, with two sides ...
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8 votes
15 answers
726 views

Equalizing fractions

When I was in grade 3, we were taught how to solve a very simple math problem. It was equaling the denominators of two or more fractions. Let's take two proper fractions:- $$ \frac{1}{2},\frac{2}{3} $$...
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  • 12k
22 votes
3 answers
542 views

Sticky polyhexes

Background A polyhex of size \$n\$ is a contiguous shape made from joining \$n\$ unit regular hexagons side-by-side. As an example, the following image (from Wikipedia) contains all 7 distinct ...
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17 votes
19 answers
1k views

Check B-powersmoothness

from Wikipedia, a number is called B-powersmooth if all prime powers \$p^v\$ that divide the number satisfy \$p^v \leq B\$. B-powersmoothness is important, for example, for Pollard's p-1 factorization ...
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8 votes
5 answers
352 views

Average impact of multiple conversion errors

Imagine four people stand in a line. The first looks at a thermometer, and tells the temperature to the person on their right. This continues down the line, until the last person writes the ...
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13 votes
11 answers
2k views

Calculate the probability of getting to the target first (exactly)

Consider the following probability puzzle. We start with a string of bits all set to 0. At each step we choose a bit uniformly and independently at random and flip it. The value your code has to ...
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25 votes
18 answers
1k views

Convert a decimal to a fraction, approximately

Take the decimal number \$0.70710678\$. As a fraction, it'd be \$\frac{70710678}{100000000}\$, which simplifies to \$\frac{35355339}{50000000}\$. If you were to make the denominator \$1\$, the closest ...
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8 votes
6 answers
683 views

Finding Distant Primes

Let us call a prime \$p\$ an \$(m,k)\$-distant prime \$(m \ge 0, k \ge 1, m,k \in\mathbb{Z})\$ if there exists a power of \$k\$, say \$k^x (x \ge 0, x \in\mathbb{Z})\$, such that \$|k^x-p| = m. \$ For ...
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  • 4,920
0 votes
3 answers
215 views

Network wide reputation survey

Given a PPCG user's user ID, calculate how much times is their Each SE site reputation is from average reputation in the Stack exchange sites they have made accounts. Let me explain, If someone's ...
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  • 12k
-5 votes
17 answers
356 views

Inverse Ax+B/Cx+D sized function

Let's assume that $$ f(x) = \frac{Ax+B}{Cx+D} $$ Where, \$x\$ is a variable and \$A\$,\$B\$,\$C\$,\$D\$ are constants. Now we have to find out the inverse function of \$f(x)\$, mathematically \$f^{-1}(...
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25 votes
10 answers
1k views

Unique half rainbows

If we take a positive integer \$n\$ and write out its factors. Someone can determine \$n\$ just from this list alone. In fact it is trivial to do this since the number is its own largest factor. ...
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18 votes
7 answers
1k views

Matching ABACABA-type patterns

(This challenge is related to the challenge "Generate the Abacaba sequence.") Zimin words (also called "sesquipowers") are an important idea in the subject of "combinatorics ...
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12 votes
7 answers
207 views

Generalised Fortunate Prime Sequences

The primorial \$p_n\#\$ is the product of the first \$n\$ primes. The sequence begins \$2, 6, 30, 210, 2310\$. A Fortunate number, \$F_n\$, is the smallest integer \$m > 1\$ such that \$p_n\# + m\$ ...
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18 votes
12 answers
946 views

Sociable sequences

Sociable numbers are a generalisation of both perfect and amicable numbers. They are numbers whose proper divisor sums form cycles beginning and ending at the same number. A number is \$n\$-sociable ...
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16 votes
30 answers
1k views

Largest power of 2 that divides \$n\$

Related, related Introduction The ruler sequence is the sequence of the largest possible numbers \$a_n\$ such that \$2^{a_n}\mid n\$. It is so-called because its pin plot looks similar to a ruler's ...
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  • 5,956
26 votes
34 answers
2k views

Semidivisibility

NOTE: Some terminology used in this challenge is fake. For two integers n and k both greater than or equal to 2 with ...
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24 votes
27 answers
2k views

Reconstruct an integer from its prime exponents

All integers \$n > 0\$ can be expressed in the form $$n = \prod_{\text{prime } p} p^e = 2^{e_2} 3^{e_3} 5^{e_5} 7^{e_7} \cdots$$ This form is also known as it's prime factorisation or prime ...
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7 votes
25 answers
534 views

Which th second now in this year

In this challenge you have to find out which nth second it is now in this year, current date and time now. Or in other words, how many seconds have passed since New Year. An example current Date is (...
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30 votes
24 answers
2k views

First sequence with no square differences

Consider the sequence \$(a_n)\$ defined in the following way. \$a_0=0\$ For all \$n=1, 2, 3, \dots\$, define \$a_n\$ to be the smallest positive integer such that \$a_n-a_i\$ is not a square number, ...
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  • 2,949
16 votes
15 answers
1k views

Generalise perfect numbers

Let \$\sigma(n)\$ represent the divisor sum of \$n\$ and \$\sigma^m(n)\$ represent the repeated application of the divisor function \$m\$ times. Perfect numbers are numbers whose divisor sum equals ...
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18 votes
7 answers
1k views

Square root multiples

This code-challenge is based on OEIS sequence A261865. \$A261865(n)\$ is the least integer \$k\$ such that some multiple of \$\sqrt{k}\$ is in the interval \$(n,n+1)\$. The goal of this challenge is ...
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  • 8,117
18 votes
18 answers
2k views

Determine the degree of a polynomial

Background: For this challenge, a polynomial looks like this: $$P(x)=a_nx^n+a_{n-1}x^{n-1}+\dots+a_2x^2+a_1x+a_0$$ The degree, \$n\$, is the highest power \$x\$ is raised to. An example of a degree 7 ...
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19 votes
11 answers
2k views

What's next, Achilles?

Powerful numbers are positive integers such that, when expressed as a prime factorisation: $$a = p_1^{e_1} \times p_2^{e_2} \times p_3^{e_3} \cdots \times p_k^{e_k}$$ all exponents \$e_1, e_2, ...\$ ...
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18 votes
5 answers
955 views

Count all binary relations

A binary relation on a set \$X\$ is simply a subset \$S \subseteq X \times X\$; in other words, a relation is a collection of pairs \$(x,y)\$ such that both \$x\$ and \$y\$ are in \$X\$. The number of ...
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  • 8,117
2 votes
0 answers
237 views

Compute the Three Dimensional Discrete Cosine Transform

Challenge I've checked that there is a question Compute the Discrete Cosine Transform which is a competition for implementing a shortest solution to compute the one dimensional discrete cosine ...
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  • 403
13 votes
14 answers
2k views

Verify the inequality!

Left in sandbox for at least 3 days. I want to verify if this inequality is true: for \$n\geq4\$, if \$a_1,a_2,a_3,\dots,a_n\in R_+\cup\{0\}\$ and \$\sum_{i=1}^na_i=1\$, then \$a_1a_2+a_2a_3+a_3a_4+\...
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13 votes
12 answers
973 views

Definite integral of polynomial functions

You will need to evaluate the definite integral (bounded by \$a\$ and \$b\$) of a certain polynomial function that takes the form of: $$\int_a^b \left( k_n x^n + k_{n-1} x^{n-1} + \cdots + k_2x^2 + ...
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  • 449
17 votes
2 answers
515 views

Count unrooted, unlabeled binary trees of n nodes

An unrooted binary tree is an unrooted tree (a graph that has single connected component and contains no cycles) where each vertex has exactly one or three neighbors. It is used in bioinformatics to ...
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  • 64.8k
2 votes
0 answers
224 views

How long to paint this house? [closed]

Here is the problem, for which I can only think of an iterative solution and have not found a closed formula: You need to paint a house with R rooms. For each room there are four walls and one ...
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18 votes
14 answers
3k views

Landau logarithm

Related: Landau's function (OEIS A000793) Background Landau's function \$g(n)\$ is defined as the largest order of permutation of \$n\$ elements, which is equal to \$\max(\operatorname{lcm}(a_1,a_2,\...
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  • 64.8k
2 votes
0 answers
359 views

Solve a Cubic Equation [closed]

Input Your program will take in the integer coefficients of the equation \$ax^3+bx^2+cx+d=0\$ as inputs (a, b, c, and d). Output All real solutions of the input equation, with an accuracy of at ...
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14 votes
20 answers
2k views

Linear integer function generator

Inspired by a recent challenge involving Fibonacci numbers in which OEIS was mentioned, I would like to present a challenge of creating a function that generates a wide array of different linear ...
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23 votes
18 answers
1k views

Interpret Interval Notation

Interval notation is a way to write complicated range bounds more conveniently and concisely than writing an inequality. The challenge, should you choose to accept it, is to write a program or ...
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  • 2,185
12 votes
5 answers
647 views

Ellipsoid surface area

Related: Ellipse circumference Introduction An ellipsoid (Wikipedia / MathWorld) is a 3D object analogous to an ellipse on 2D. Its shape is defined by three principal semi-axes \$a,b,c\$: $$ \frac{x^2}...
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  • 64.8k
18 votes
27 answers
1k views

Output a unique sign sequence

A sign sequence is an infinite sequence consisting entirely of \$1\$ and \$-1\$. These can be constructed a number of ways, for example: Alternating signs: \$1, -1, 1, -1, ...\$ \$-1\$ for primes, \$...
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20 votes
28 answers
1k views

Partial sums of the Kempner series

The Kempner series is a series that sums the inverse of all positive integers that don't contain a "9" in their base-10 representations (i.e., \$\frac{1}{1} + \frac{1}{2} + \frac{1}{3} + .. +...
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29 votes
2 answers
1k views

Golf the smallest sphere!

Inspired by this challenge, as well as a problem I've been working on Problem: Given a non-empty set of points in 3D space, find the diameter of the smallest sphere ...
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  • 361
12 votes
7 answers
657 views

Generalised Taxicab Numbers

\$\newcommand{T}[1]{\text{Ta}(#1)} \newcommand{Ta}[3]{\text{Ta}_{#2}^{#3}(#1)} \T n\$ is a function which returns the smallest positive integer which can be expressed as the sum of 2 positive integer ...
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22 votes
2 answers
2k views

Eye test - How many squares are in this picture?

The picture: Sick of the same old grid where the answer is simply a square pyramidal number? Accept the challenge and write a program that given a positive integer \$n\$ counts how many squares are ...
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  • 2,153
12 votes
18 answers
1k views

Polynomial Laplace transform

This is a repost of this challenge, intended to revamp it for looser I/O formats and updated rules You are to write a program which takes an integer polynomial in \$t\$ as input and outputs the ...
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16 votes
4 answers
981 views

(Almost) Solve Fermat's Last Theorem

It's a well-known fact that Fermat's Last Theorem is true. More specifically, that for any integer \$n \gt 2\$, there are no three integers \$a, b, c\$ such that $$a^n + b^n = c^n$$ However, there are ...
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23 votes
28 answers
3k views

"Factorise" a quadratic [duplicate]

When learning to factorise quadratics in the form \$x^2 + ax + b\$, a common technique is to find two numbers, \$p, q\$ such that $$pq = b \\ p + q = a$$ as, for such numbers, \$x^2 + ax + b = (x + p)(...
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22 votes
19 answers
2k views

For what block sizes is this checksum valid?

The input: As an example, take a list containing a number of bits (in this case, 32): 11000010000100111011000011001011 We can calculate a simple checksum of this ...
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23 votes
27 answers
2k views

Perfect radicals

Given a positive integer number \$n\$ output its perfect radical. Definition A perfect radical \$r\$ of a positive integer \$n\$ is the lowest integer root of \$n\$ of any index \$i\$: $$r = \sqrt[i]{...
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  • 9,486
40 votes
67 answers
5k views

Infinitely many ℕ

Background: A sequence of infinite naturals is a sequence that contains every natural number infinitely many times. To clarify, every number must be printed multiple times! The Challenge: Output a ...
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17 votes
20 answers
2k views

Find distance between the closest 3D points

Your task is to take \$n \ge 2\$ points in 3D space, represented as 3 floating point values, and output the Euclidean distance between the two closest points. For example $$A = (0, 0, 0) \\ B = (1, 1, ...
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  • 387
18 votes
13 answers
1k views

All-inclusive semi-primes

\$723 = 3 \times 241\$ is a semi-prime (the product of two primes) whose prime factors include all digits from \$1\$ to \$n\$, where \$n\$ is the total number of digits between them. Another way to ...
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2 votes
0 answers
132 views

Dobble Double Challenge [closed]

I have a problem, which I haven't found a solution for. Solutions to the first part are well documented, but I have yet to find anyone who has solved the second part. I call this the "Dobble"...
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12 votes
7 answers
2k views

Fastest square root of an arbitrary size

We do seem to have a fastest square root challenge, but it's very restrictive. In this challenge, your program (or function) will be given an arbitrarily sized nonnegative integer, which is the square ...
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34 votes
23 answers
3k views

Narcissistic loop lengths

A narcissistic number is a natural number which is equal to the sum of its digits when each digit is taken to the power of the number digits. For example \$8208 = 8^4 + 2^4 + 0^4 + 8^4\$, so is ...
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