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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].

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4
votes
1answer
155 views

How wavy is an array?

A wave of power \$k\$ is an infinite array that looks like \$1,2,\dots,k,k-1,\dots,1,\dots,k,\dots,1,\dots\$, and so on. For example, a wave of power 3 starts with \$1,2,3,2,1,2,3,2,1,...\$, and ...
24
votes
14answers
3k views

Are my triangles similar?

Given (in any structure; flat list, two lists of lists, a tuple of matrices, a 3D array, complex numbers,…) the coordinates for two non-degenerate triangles ...
22
votes
9answers
2k views

Fermat's polygonal number theorem

Fermat's polygonal number theorem states that every positive integer can be expressed as the sum of at most \$n\$ \$n\$-gonal numbers. This means that every positive integer can be expressed as the ...
15
votes
41answers
3k views

Find the percentage

We haven't had any nice, easy challenges in a while, so here we go. Given a list of integers each greater than \$0\$ and an index as input, output the percentage of the item at the given index of the ...
35
votes
50answers
7k views

I reverse the source code, you negate the input!

Blatant rip-off of a rip-off. Go upvote those! Your task, if you wish to accept it, is to write a program/function that outputs/returns its integer input/argument. The tricky part is that if I ...
15
votes
7answers
1k views

Decimal “XOR” operator

Many programming language provide operators for manipulating the binary (base-2) digits of integers. Here is one way to generalize these operators to other bases: Let x and y be single-digit numbers ...
13
votes
11answers
726 views

Output Distinct Factor Cuboids

Output Distinct Factor Cuboids Today's task is very simple: given a positive integer, output a representative of each cuboid formable by its factors. Explanations A cuboid's volume is the product ...
8
votes
11answers
685 views

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 ...
16
votes
14answers
1k views

Permutations in Disguise

Given a \$n\$-dimensional vector \$v\$ with real entries, find a closest permutation \$p\$ of \$(1,2,...,n)\$ with respect to the \$l_1\$-distance. Details If it is more convenient, you can use ...
20
votes
40answers
3k views

Parallel resistance in electric circuits

Introduction: Two resistors, R1 and R2, in parallel (denoted R1 || R2) have a combined ...
17
votes
8answers
1k views

Dividing Divisive Divisors

Given a positive integer \$n\$ you can always find a tuple \$(k_1,k_2,...,k_m)\$ of integers \$k_i \geqslant 2\$ such that \$k_1 \cdot k_2 \cdot ... \cdot k_m = n\$ and $$k_1 | k_2 \text{ , } k_2 | ...
31
votes
21answers
6k views

Random point on a sphere

The Challenge Write a program or function that takes no input and outputs a vector of length \$1\$ in a theoretically uniform random direction. This is equivalent to a random point on the sphere ...
16
votes
12answers
5k views

Divide Numbers by 0

We've all been told at some point in our lives that dividing by 0 is impossible. And for the most part, that statement is true. But what if there was a way to perform the forbidden operation? Welcome ...
19
votes
12answers
2k views

Calculate Landau's function

Landau's function \$g(n)\$ (OEIS A000793) gives the maximum order of an element of the symmetric group \$S_n\$. Here, the order of a permutation \$\pi\$ is the smallest positive integer \$k\$ such ...
9
votes
2answers
372 views

​Plane​ ​Blow​up​

The Blow-up is a powerful tool in algebraic geometry. It allows the removal of singularities from algebraic sets while preserving the rest of their structure. If you're not familiar with any of that ...
19
votes
4answers
444 views

Compute height of Bowl Pile

Bowl Pile Height The goal of this puzzle is to compute the height of a stack of bowls. A bowl is defined to be a radially symmetric device without thickness. Its silhouette shape is an even ...
9
votes
0answers
172 views

Decompose Commutators

A theorem in this paper1 states that every integral n-by-n matrix M over the integers with trace M = 0 is a commutator, that means there are two integral matrices A,B of the same size ...
2
votes
1answer
161 views

Black and white shirt 2

This is a more complicated version of this puzzle. The premise is the same but a few rules differ in a few key places, making for a more complex problem. Assume I have some number of black shirts and ...
1
vote
7answers
383 views

Black and white shirts

This puzzle is based on this Math.SE post. A more complex version of this problem can be found over here. Assume I have some number of black shirts and some number of white shirts, both at least 1. ...
38
votes
3answers
3k views

Construct a pentagon avoiding compass use

Rules You will start with only two elements: Points \$A\$ and \$B\$ such that \$A \neq B\$. These points occupy a plane that is infinite in all directions. At any step in the process you may do any ...
5
votes
4answers
423 views

Find X,Y,Z coordinates from index

Introduction I began studying the Collatz Conjecture And noticed these patterns; 0,1,2,2,3,3...A055086, and 0,1,2,0,3,1...A082375, in the numbers that go to 1 in one odd step, 5,10,20,21,40,42......
3
votes
1answer
274 views

Multiplication in Brainfuck - minimum number of evaluations [closed]

Given two numbers in tape location #0 and tape location #1 in Brainfuck, compute their product into another tape location (specify with answer). Optimize for the least amount of time-units used, where ...
-4
votes
4answers
104 views

One square root function for unsigned numbers [closed]

One square root function for unsigned numbers Write the function sqrti(x) that from one not negative integer number x, it returns the integer square root of that number truncate to the 0 digit, so ...
4
votes
0answers
102 views

Make a slow monotonic injection [duplicate]

In 256 bytes or fewer write a function, \$f\$, from the positive integers to the positive integers that is: Monotonic: larger inputs always map to larger outputs. (\$a < b \implies f(a) < f(b)\$...
5
votes
2answers
310 views

Golf my iteration function

Here is my ungolfed Ruby code for a function I want to try and golf: ...
23
votes
19answers
3k views

Analog is Obtuse!

An analog clock has 2 hands*: Hour and minute. These hands circle the clock's face as time goes by. Each full rotation of the minute hand results in 1/12th of a rotation of the hour hand. 2 full ...
10
votes
22answers
2k views

Find the C-factor of a vote

In this challenge you will be determining how controversial a vote is, given an array of other votes, by figuring out a number called the C-factor. What is the C-factor, you ask? Well, imagine you've ...
8
votes
1answer
272 views

Partition and Restructure

Given two contiguous shapes of the same area, determine the optimal way to divide the first shape into a minimum number of contiguous segments such that they can be rearranged to form the second shape....
11
votes
21answers
1k views

An OEIS polyglot

This is an answer-chaining challenge relating to the OEIS. Oh, the justification for this is because a company needs one program to print out their OEIS sequences real bad and they have every ...
92
votes
12answers
8k views

Proving that a Russian cryptographic standard is too structured

The aim of this challenge is to find an impossibly short implementation of the following function p, in the langage of your choosing. Here is C code implementing it ...
3
votes
1answer
213 views

Multiplication in the Steenrod Algebra

Here's yet another Steenrod algebra question. Summary of the algorithm: I have a procedure that replaces a list of positive integers with a list of lists of positive integers. You need to repeatedly ...
16
votes
11answers
1k views

Generate basis elements of the Steenrod algebra

The Steenrod algebra is an important algebra that comes up in algebraic topology. The Steenrod algebra is generated by operators called "Steenrod squares," one exists for each positive integer i. ...
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
200 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
626 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 ...
17
votes
23answers
1k 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 \$...
10
votes
6answers
1k views

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
5k 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 ...
28
votes
26answers
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 ...
1
vote
0answers
152 views

How many right triangles can you find? [closed]

Challenge You will be given an input represented by x, which is a string containing at least 3 characters. It will consist only of the standard numeric characters, ...
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
101 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
121 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 ...
41
votes
20answers
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
270 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
334 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 ...
45
votes
50answers
4k 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 ...