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Questions tagged [math]

The challenge involves mathematics. Also consider using more specific tags: [number] [number-theory] [arithmetic] [combinatorics] [graph-theory] [geometry] [abstract-algebra].

20
votes
16answers
3k views

​Cuban​ ​Primes

Given a natural number \$n\$, return the \$n\$-th cuban prime. Cuban Primes A cuban prime is a prime number of the form $$p = \frac{x^3-y^3}{x-y}$$ where \$y>0\$ and \$x = 1+y\$ or \$x = 2+y\$ ...
0
votes
3answers
186 views

Roots of Arbitrary Numbers [closed]

One day, when I was bored in maths class, I learned of a neat trick for solving the real cube root of a number! Let's use the number \$79,507\$ as an example. First, take digit in the one's place ...
14
votes
16answers
585 views

Dihedral group D4 composition with custom labels

The dihedral group \$D_4\$ is the symmetry group of the square, that is the moves that transform a square to itself via rotations and reflections. It consists of 8 elements: rotations by 0, 90, 180, ...
13
votes
13answers
2k views

A factorization game

Input A single integer \$1 \leq x \leq 10^{15}\$. Output The maximum number of distinct positive integers that have the product \$x\$. Examples Input: 1099511627776. Output: 9. One possible ...
22
votes
23answers
3k views

Upside-Down Pyramid Addition…REVERSED!

Upside-Down Pyramid Addition is the process of taking a list of numbers and consecutively adding them together until you reach one number. When given the numbers ...
16
votes
22answers
902 views

Enumerate Derangements

Given some positive integer \$n\$ generate all derangements of \$n\$ objects. Details A derangement is a permutation with no fixed point. (This means in every derangement number \$i\$ cannot be in ...
32
votes
21answers
2k views

A ​Note ​on ​N!

J. E. Maxfield proved following theorem (see DOI: 10.2307/2688966): If \$A\$ is any positive integer having \$m\$ digits, there exists a positive integer \$N\$ such that the first \$m\$ digits of \$...
9
votes
6answers
1k views
+150

Which really big number is bigger?

This question is tricky (and in particular harder than Which big number is bigger?), for those who like more challenging puzzles. Input Integers a1, a2, a3, a4, a5, b1, b2, b3, b4, b5 each in the ...
35
votes
21answers
4k views

Amount of permutations on an NxNxN Rubik's Cube

Introduction: A 3x3x3 Rubik's Cube has \$43,252,003,274,489,856,000\$ possible permutations, which is approximately 43 quintillion. You may have heard about this number before, but how is it actually ...
24
votes
21answers
2k views

Fundamental Solution of the Pell Equation

Given some positive integer \$n\$ that is not a square, find the fundamental solution \$(x,y)\$ of the associated Pell equation $$x^2 - n\cdot y^2 = 1$$ Details The fundamental \$(x,y)\$ is a pair ...
14
votes
14answers
1k views

Multiply Two Integer Polynomials

Your task is to take two single-variable integer polynomial expressions and multiply them into their unsimplified first-term-major left-to-right expansion (A.K.A. FOIL in the case of binomials). Do ...
0
votes
0answers
100 views

Compute the order of a Rubik's Cube cycle without trivially counting them [duplicate]

On a Rubik's Cube, performing a particular sequence of moves repeatedly will always return it to its original state. Your job is to figure out the "order" of a particular sequence of moves, that is, ...
-1
votes
2answers
115 views

Find efficient seating arrangement in a line [closed]

We have X Girls and Y Boys in a class. If more girls sit together they will not behave. Similarly if more boys sit together they will not behave. Write a program/algorithm to get maximum same gender ...
39
votes
19answers
5k views

Calculate the Mean mean of two numbers

disclaimer: the Mean mean is made up by me Define the arithmetic mean of \$n\$ numbers as $$M_1(x_1,...,x_n)=\frac{x_1+x_2+...+x_n}{n}$$ Define the geometric mean of \$n\$ numbers as $$M_0(x_1,...,...
1
vote
4answers
254 views

Nearest hamming cycle period in MD5

This riddle was inspired by that thread. Consider that you are super-hacker and try to break MD5 hashing algorithm by looking for a hash collisions for a given hash string which your friend gave to ...
15
votes
2answers
251 views

Japanese Multiplication [duplicate]

There's a visual method for multiplication that is taught to Japanese schoolchildren [citation needed] that uses lines and crossings to get the answer. Image Source Your task is to implement this in ...
44
votes
47answers
3k views

Multiplicative persistence

Multiplicative Persistence Multiply all the digits in a number Repeat until you have a single digit left As explained by Numberphile: Numberphile "What's special about 277777788888899?" Numberphile ...
2
votes
1answer
173 views

Find all diagonal counts in only one direction [closed]

If I need to get the number of diagonal squares in all directions: I do the following formula 2 N − 2 − |x − y| − |x + y − N − 1| The above example has 13 and ...
22
votes
1answer
1k views

Is it possible to make a clamp function shorter than a ternary in JS?

Imagine this short function to clamp a number between 0 and 255: c = n => n > 0 ? n < 255 ? n : 255 : 0 Is this the shortest possible version of a clamp ...
25
votes
28answers
3k views

Make me a metasequence

Background For this challenge, a 'metasequence' will be defined as a sequence of numbers where not only the numbers themselves will increase, but also the increment, and the increment will increase ...
15
votes
16answers
621 views

Compound Interest… with Wizard Money

Gringotts isn't just a vault, but a reputable financial institution and wizards need loans too. Since you don't want to be screwed over by the Gringotts goblins, you decided it would be a good idea to ...
33
votes
5answers
8k views

Historical difference between `/` and `÷` in mathematical expressions

Introduction: Inspired by a discussion that is already going on for many years regarding the expression \$6÷2(1+2)\$. With the expression \$6÷2(1+2)\$, mathematicians will quickly see that ...
7
votes
7answers
528 views

Check type of an integer

You will receive an integer less than 2000000000 and bigger than -2000000000 and you have to test what type(s) of number this is out of: ...
10
votes
10answers
555 views

Fizzbuzz in any base

Challenge Input: An integer \$b\$ between 2 and 62 (inclusive). Output: Count from \$1\$ to the equivalent of \$5000_{10}\$ in base \$b\$, using any reasonable representation for the digits. ...
21
votes
12answers
1k views

Indexing the Extended Fibonacci Numbers

You've probably heard of Fibonacci numbers. Ya know, that integer sequence that starts with 1, 1, and then each new number is the sum of the last two? ...
6
votes
5answers
291 views

Generate the k-ary necklaces of length n

The set of necklaces is the set of strings, where two strings are considered to be the same necklace if you can rotate one into the other. Your program will take nonnegative integers ...
1
vote
2answers
200 views

Work out \$x^y\$ using only addition and subtraction [duplicate]

The challenge is to implement a function or program that takes two numbers, \$x\$ and \$y\$ and return the result of \$x^y\$. The program cannot use any other mathematical operation other than \$+\$ ...
5
votes
1answer
297 views

Surreal Numbers

Surreal Numbers Surreal numbers are one way of describing numbers using sets. In this challenge you will determine the value of a surreal number. Intro A surreal number consists of two sets: a left ...
9
votes
0answers
111 views

Order of Elements of the Rubik's Cube [duplicate]

Introduction All the possible moves and their combinations of a Rubik's Cube form a group. A group in general is a set with some binary operation defined on it. It must contain a neutral element with ...
0
votes
0answers
46 views

Polynomial to String [duplicate]

I'm new to code-golf, but I was trying to solve this problem myself, and thought there must be a much "better"/shorter way of doing it. Given a sequence (list) of numbers \$a_0, a_1,\cdots,a_n\$, ...
2
votes
3answers
128 views

All the digisibles [duplicate]

A natural number (written in the decimal base) is qualified as digisible if and only if it fulfills the following 3 conditions: none of its digits is zero, all the digits that compose it are ...
20
votes
20answers
1k views

Smallest Diversifying Exponent

A pandigital number is an integer which contains every digit from 0 to 9 at least once. 1234567890, 1902837465000000, and 9023289761326634265 are all pandigital. For the purposes of this challenge, ...
14
votes
25answers
1k views

Standardize the Samples (Compute the z-Score)

Given a list of floating point numbers, standardize it. Details A list \$x_1,x_2,\ldots,x_n\$ is standardized if the mean of all values is 0, and the standard deviation is 1. One way to compute this ...
-2
votes
2answers
149 views

find the value at kth position when numbers are sorted lexicographically till n [closed]

Ex :- Input: n = 12, k = 5 Output: ans = 2 Sorted list S: ["1", "10", "11", "12", "2", "3", "4", "5", ...., "9"] ans = 2
1
vote
4answers
199 views

Round the digits last digit, over and over

Challenge: Given two inputs, x and y, round x to one less significant figure, then repeat until it has y number of unrounded digits left. (the decimal point does not count as a digit) Input & ...
18
votes
31answers
5k views

Find the number of leading zeroes in a 64-bit integer

Problem: Find the number of leading zeroes in a 64-bit signed integer Rules: The input cannot be treated as string; it can be anything where math and bitwise operations drive the algorithm The ...
13
votes
1answer
980 views

Golf a number bigger than Loader's number

As a follow up to Shortest terminating program whose output size exceeds Graham's number and Golf a number bigger than TREE(3), I present a new challenge. Loader's number is a very large number, ...
21
votes
26answers
2k views

Digital Sumorial

Given an input n, write a program or function that outputs/returns the sum of the digital sums of n for all the bases 1 to ...
25
votes
6answers
1k views

Prime containment numbers (speed edition)

This is sequence A054261 The \$n\$th prime containment number is the lowest number which contains the first \$n\$ prime numbers as substrings. For example, the number \$235\$ is the lowest number ...
21
votes
14answers
2k views

Prime containment numbers (golf edition)

This is sequence A054261. The \$n\$th prime containment number is the lowest number which contains the first \$n\$ prime numbers as substrings. For example, the number \$235\$ is the lowest number ...
20
votes
38answers
2k views

Given an input, print all exponents where the base and power sum to the input

So this is my first challenge on this site. The challenge is to take in an input integer \$n\$, which will be positive, and print, in ascending order (\$1\$ to \$n\$, including n), the output of \$i^{...
11
votes
3answers
407 views

Is it an arithmetico-geometric sequence?

An arithmetico-geometric sequence is the elementwise product of an arithmetic sequence and a geometric sequence. For example, 1 -4 12 -32 is the product of the ...
-4
votes
1answer
267 views

Compound interest with additions [closed]

You have been given the charge to calculate the current balance as of the day that you perform the calculation for 330,000 individuals who worked for an average of 30 years spanning 300 years where ...
18
votes
8answers
767 views

Is this quadrilateral cyclic?

In mathematics, a cyclic quadrilateral is one whose vertices all lie on the same circle. In other words, every vertex is on the circumcircle of the other three. For more information, see the MathWorld ...
19
votes
13answers
1k views

Dirichlet Convolution

The Dirichlet convolution is a special kind of convolution that appears as a very useful tool in number theory. It operates on the set of arithmetic functions. Challenge Given two arithmetic ...
12
votes
11answers
2k views

Quaternion square root

Background Quaternion is a number system that extends complex numbers. A quaternion has the following form $$ a + bi + cj + dk $$ where \$ a,b,c,d \$ are real numbers and \$ i,j,k \$ are three ...
19
votes
27answers
3k views

Strange Addition

Challenge Calculate the strange sum of two natural numbers (also known as lunar addition): Given A=... a2 a1 a0 and ...
14
votes
28answers
2k views

The inverse Collatz Conjecture

I think the Collatz Conjecture is already well-known. But what if we invert the rules? Start with an integer n >= 1. Repeat the following steps: If n is even, multiply it by 3 and add 1. If n is ...
15
votes
40answers
2k views

Sum square difference

The sum of the squares of the first ten natural numbers is, \$1^2 + 2^2 + \dots + 10^2 = 385\$ The square of the sum of the first ten natural numbers is, \$(1 + 2 + ... + 10)^2 = 55^2 = 3025\$ ...
0
votes
0answers
58 views

Multiples of 3 or 5 [duplicate]

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. For a given input n, find the sum of multiples of 3 or five between 1 ...