Questions tagged [math]
The challenge involves mathematics. Also consider using more specific tags: [number] [number-theory] [arithmetic] [combinatorics] [graph-theory] [geometry] [abstract-algebra].
1,332
questions
13
votes
1answer
173 views
Can this knot be colored with 3 colors?
In this challenge you will be asked to take a knot and determine if it can be colored in a particular way.
First we draw a diagram of the knot. We use the standard way of drawing knots where we put ...
26
votes
5answers
2k views
Longest Prime Sums
Sandbox
There are special sets S of primes such that \$\sum\limits_{p\in S}\frac1{p-1}=1\$. In this challenge, your goal is to find the largest possible set of primes that satisfies this condition.
...
14
votes
15answers
2k views
Smallest Fibonacci Multiples
Sandbox
Background (not necessary for the challenge)
A standard number theory result using the pigeonhole principle is the fact that given any natural number k, there is a Fibonacci number that is a ...
-2
votes
6answers
193 views
Interpreting the Wolfram Code
Introduction
An elementary cellular automaton is a cellular automaton that is 1-dimensional and has 2 states, 1 and 0. These cellular automata are categorized based on a simple code: the Wolfram code,...
14
votes
15answers
2k views
Roll for Initiative!
Roll for Initiative!
Introduction
In tabletop games like Dungeons and Dragons, when you begin a battle, all involved parties roll for initiative. In DnD 5e, this is ...
16
votes
1answer
448 views
Find the number of n-by-n (-1, 0, 1) matrices with zero permanent as quickly as possible
The permanent of an \$n\$-by-\$n\$ matrix \$A = (a_{i,j})\$ is defined as:
$$\operatorname{perm}(A)=\sum_{\sigma\in S_n}\prod_{i=1}^n a_{i,\sigma(i)}$$
For a fixed \$n\$, consider the \$n\$-by-\$n\$ ...
32
votes
28answers
3k views
How many times, are they multiples?
You are given three parameters: start(int), end(int) and list(of int);
Make a function that returns the amount of times all the numbers between start and end are multiples of the elements in the list....
15
votes
3answers
2k views
How divisible are you?
You are to create a program which, when given a positive integer \$n\$, outputs a second program. This second program, when run, must take a second positive integer \$x\$ and output one of two ...
17
votes
4answers
1k views
Can Alice win the game?
Can Alice win the game?
The game's rules are as follows. First, a finite non empty set of positive integers \$X\$ is defined. Then, Alice and Bob take turns choosing positive integers, with Alice ...
28
votes
4answers
4k views
How close are we, really?
Please note: this is a restricted-source challenge — see details below!
Each natural number \$n\$ has 10 faces: its decimal representations in bases \$1\$ through to \$10\$. For example, the 10 faces ...
12
votes
8answers
494 views
Decorate Pascal's Triangle
Although what is a Pascal's triangle is well-known and we already can generate it, the task is now different:
Output \$n\$ first lines of the Pascal's triangle as colored bricks.
Color number is ...
-4
votes
0answers
62 views
A simple calculator [duplicate]
Make a simple calculator which does the basic math operations +, -, * /, one at the time:
Input example: 10+12
Output: 22
Of course, lightest code wins.
Good luck!
2
votes
1answer
117 views
Gaussian integer division reminder [closed]
Gaussian integer is a complex number in the form \$x+yi\$, where \$x,y\$ are integer and \$i^2=-1\$.
The task is to perform such operation for Gaussian integers \$a,b\$, that
\$a=q \cdot b+r\$ and \$|...
11
votes
23answers
2k views
N-Dimensional Cartesian Product
Introduction
The Cartesian product of two lists is calculated by iterating over every element in the first and second list and outputting points. This is not a very good definition, so here are some ...
11
votes
9answers
950 views
Area of diagonal-folded regular polygon
I have a piece of paper whose shape is a regular n-gon with side length 1. Then I fold it through some of its diagonals. What is ...
2
votes
5answers
226 views
Proportion of strings with ascending letters [closed]
Challenge
Construct n strings, each with three distinct letters, chosen randomly with equal probability.
Print the proportion ...
15
votes
58answers
4k views
Average Two Letters
Introduction
Every letter in the English alphabet can be represented as an ASCII code. For example, a is 97, and ...
9
votes
8answers
338 views
1D Shikaku Validation
Shikaku is a 2D puzzle. The basic rundown of it is that a rectangular grid has some numbers in it, and you want to partition the grid into rectangular components such that each component contains ...
8
votes
13answers
359 views
Print all the ways to aquire specific number using only specific numbers
Let's say we have some arbitrary number:
For example 25. We also have some "tokens" (poker chips, money, something similar) with different values.
Values of tokens are
...
14
votes
13answers
1k views
Is it rectilinear?
Today's challenge:
Given an ordered list of at least 3 unique integer 2D points forming a polygon, determine if the resulting polygon is Rectilinear.
A polygon is rectilinear if every interior ...
27
votes
18answers
4k views
Fermat's Last Theorem, mod n
Fermat's Last Theorem, mod n
It is a well known fact that for all integers \$p>2\$, there exist no integers \$x, y, z>0\$ such that \$x^p+y^p=z^p\$. However, this statement is not true in ...
10
votes
4answers
1k views
How compactly can your language perform accurate numerical integration?
WARNING: This challenge may need 128 bit floats.1
The task is to perform numerical integration. Consider the following three functions.
\$
f(x) = cx^{c - 1}e^{-x^c}
\$
\$
g_1(x) = 0.5e^{-x}
\$
\$...
0
votes
1answer
126 views
Shooting gallery Puzzle!
Have you been shooting gallery? We are recently.
In our shooting gallery cans and aluminum cans from under various drinks hang and stand. More precisely, they hung and stood.
From our shots, banks ...
6
votes
4answers
313 views
Shorthand Combined Functions
I was doing some investigation into trig functions using compound angles recently, and noticed that the results are really long and tedious to write:
$$
\cos(A+B) = \cos A \cos B - \sin A \sin B \\
\...
9
votes
3answers
473 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 ...
24
votes
10answers
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
43answers
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 ...
36
votes
52answers
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
768 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
713 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 ...
17
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
42answers
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
379 views
Plane Blowup
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
449 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 ...
13
votes
1answer
289 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
384 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
4k 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
430 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
282 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
105 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
316 views
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 ...
