Questions tagged [math]
The challenge involves mathematics. Also consider using more specific tags: [number] [number-theory] [arithmetic] [combinatorics] [graph-theory] [geometry] [abstract-algebra].
1,365
questions
15
votes
14answers
1k views
Generating generating expressions for sequences
(yes, "generating generating" in the title is correct :) )
Context
In middle (?) school we are taught about sequences and, in particular, we are taught about linear sequences where the ...
12
votes
14answers
2k views
Pseudo-deterministic number generator
Task
Write a function/full program that will be able to produce two different sequences of integers in [0, ..., 9]. You will take an input ...
5
votes
0answers
183 views
2D interpolation
Given required values for an expression with 2 variables, output a short expression which fulfill these values
Input
You may take the input in any reasonable format, e.g. ...
10
votes
10answers
680 views
Find how many ordered pairs of integers share only one digit
Task
Your task is to make the smallest function/program that can, when gives an number N, return/print:
the number of possible choices a, b such that \$1 \leq a &...
15
votes
10answers
1k views
Shortest total non-primitive recursive function
Natural numbers ≡ \$\mathbb{N}≡\{0,1,2,...\}\$
The submission can be either a program or a function, both cases will henceforth be referred to as "function".
The task is to golf the shortest ...
-2
votes
7answers
181 views
Generate this expanding series [closed]
Challenge
Your task is to generate a string using this sequence:
1,1,2,1,1,2,3,2,1,1,3,2,4,2,3,1,....
Which is more understandable in this format:
...
2
votes
15answers
539 views
Convert a decimal integer to binary only using arithmetic operators
There are 10 types of people in the world, those who understand binary and those who do not.
Where are you? Let's see!
Challenge
Your task is to convert a decimal integer to binary, only using a ...
17
votes
16answers
876 views
(RGS 4/5) Inverting matrices modulo m
Task
Given an integer matrix M and a modulus m, find an inverse of M modulo ...
10
votes
34answers
2k views
Find the number of integers in the range from 1 to N that ends with 2
Task
As input you have:
a positive integer N
And you should output:
The number of integers in \$[1,N]\$ (an inclusive range) which end with the digit \$2\$ in ...
5
votes
2answers
276 views
Your Oscilloscope has ExPloDEd ! Make a sine wave [closed]
[ CODE GOLF]
BAM! - Fire and Smoke
Your Oscilloscope has exploded from one too many waves.
Re-create these waves assuming the following:
All waves are Sine Waves
An amplitude of ...
15
votes
15answers
1k views
Square-Cube Digit Usage
The point of this challenge is to find the smallest positive integer that uses up at least all of the digits supplied in the input after it is squared and cubed.
So, when provided an input such as <...
20
votes
8answers
974 views
Counting Distinct Real Roots of Low-Degree Polynomials
Challenge: I want to know about the real roots of polynomials. As a pure mathematician, I care about the existence of such roots, rather than their numeric values.
The challenge is to write the ...
9
votes
5answers
476 views
Computing a specific coefficient in a quotient of polynomials
Context
After "Computing a specific coefficient in a product of polynomials", asking you to compute a specific coefficient of polynomial multiplication, I wish to create a "mirror" challenge, asking ...
38
votes
13answers
3k views
7
votes
0answers
346 views
Finding Radical Ideals
Sandbox
Finding radicals of arbitrary ideals in rings is hard! However, it's a doable task in polynomial rings, since they are Noetherian (all ideals are finitely generated)
Background
A quick ...
15
votes
26answers
2k views
Drawing one-liner
CodeDrawing one-liner
Teaser
Behold this formidable drawing:
Can you draw this in a single stroke? Give it a try.
Can you do this one, now:
Give it a try.
How it works
These "make this drawing ...
12
votes
9answers
1k views
Integer Logarithm
Objective
Take \$a \in ℤ_{>1}\$ and \$b \in ℤ_+\$ as inputs. Write a function \$f\$ such that:
$$
f(a,b) =
\left\{
\begin{array}{ll}
\log_ab & \quad \text{if} \space \log_ab \in ℚ ...
36
votes
37answers
8k views
Is this a triangle?
Task
Write a function/program that, given three positive integers a, b and c, prints a ...
34
votes
37answers
5k views
Lonely Multiplication
Based on this question from Code Review.
Given precisely three positive integers, return the product of all of the distinct inputs. If none of the inputs are distinct, return 1. That is, implement ...
30
votes
29answers
5k views
How far should I sum?
How far should I sum?
The harmonic series is the "infinite sum" of all the fractions of the form \$\frac1n\$ for \$n\$ positive integer. I.e. the harmonic series is
$$\frac11 + \frac12 + \frac13 + \...
3
votes
1answer
232 views
Estimate the mean minimum Hamming distance
Task
Inputs \$b \leq 100\$ and \$n \geq 2\$. Consider \$n\$ binary strings, each of length \$b\$ sampled uniformly and independently. We would like to compute the expected minimum Hamming distance ...
27
votes
24answers
4k views
Calculate the Progressive Mean™
Disclaimer: This challenge is inspired by a coding error I once made.
Okay, time for a maths lesson. A normal mean average looks like this:
...
14
votes
14answers
882 views
Computing a specific coefficient in a product of polynomials
Generator functions
This gives the context for why this challenge came to life. Feel free to ignore.
Generator functions are a nice way of encoding the solution to a problem of combinatorics. You ...
-6
votes
5answers
301 views
Approximating the amount of prime numbers below `x`
Background
We define the prime-counting function, \$\pi(x)\$, as the number of prime numbers less than or equal to \$x\$. You can read about it here.
For example, \$\pi(2) = 1\$ and \$\pi(6) = 3\$.
...
34
votes
35answers
6k views
Shift right by half a bit
The challenge is to implement a program or function (subsequently referred to as "program") that takes a nonnegative integer \$n\$ as input and returns \$n\over\sqrt{2}\$ (the input divided by the ...
7
votes
1answer
509 views
Average number of strings with Levenshtein distance up to 4
This is a version of this question which should not have such a straightforward solution and so should be more of an interesting coding challenge. It seems, for example, very likely there is no easy ...
17
votes
10answers
411 views
Decomposition of a matrix in \$ SL_2(\mathbb{Z}) \$
Background
The special linear group \$ SL_2(\mathbb{Z}) \$ is a multiplicative group of \$ 2 \times 2 \$ matrices whose elements are integers and determinant is 1.
It is known that every member of \$...
2
votes
0answers
52 views
Compositional inverse of a power series [duplicate]
If \$f(x) = x + \sum_{i>1} a_ix^i\$ and \$g(x)=x+\sum_{i>1}b_ix^i\$ then there is a composite power series \$f(g(x))\$ also of this form. Given a power series \$f\$ the goal is to find a ...
20
votes
21answers
5k views
Largest monetary amount impossible to make with two types of coin
Suppose we have two different types of coin which are worth relatively prime positive integer amounts. In this case, it is possible to make change for all but finitely many quantities. Your job is to ...
15
votes
8answers
1k views
Is this quadrilateral tangential?
Related: Is this quadrilateral cyclic?
Background
A tangential quadrilateral is a quadrilateral which has an incircle:
Examples include any square, rhombus, or a kite-like shape. Rectangles or ...
12
votes
4answers
2k views
Can you calculate the average Levenshtein distance exactly?
The Levenshtein distance between two strings is the minimum number of single character insertions, deletions, or substitutions to convert one string into the other one.
The challenge is to compute ...
6
votes
1answer
581 views
Average number of strings with Levenshtein distance up to 3
The Levenshtein distance between two strings is the minimum number of single character insertions, deletions, or substitutions to convert one string into the other one. Given a binary string \$S\$ of ...
11
votes
1answer
255 views
Maximal 2-distance Sets
In the plane (\$\mathbb R^2\$) we can have at most five distinct points such that the distances from each point to every other point (except itself) can assume at most two distinct values.
An example ...
15
votes
1answer
514 views
Is this ordinal prime?
You are given an countable ordinal \$1 < r < \varepsilon_0\$. Determine whether or not it is prime. If not, provide exactly two ordinals \$r_0, r_1 < r\$ such that \$r_0r_1 = r\$, following ...
13
votes
5answers
636 views
Define the finite field GF(9)
\$GF(9)\$ or \$GF(3^2)\$ is the smallest finite field whose order isn't a prime or a power of two. Finite fields of prime order aren't particurlarly interesting and there are already challenges for \$...
16
votes
1answer
254 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 ...
29
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.
...
21
votes
19answers
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
7answers
337 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,...
17
votes
17answers
3k 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 ...
18
votes
2answers
646 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\$ ...
34
votes
28answers
4k 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....
16
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 ...
18
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 ...
29
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 ...
14
votes
8answers
540 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 ...
3
votes
1answer
128 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 \$|...
12
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 ...
12
votes
9answers
991 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 ...
3
votes
5answers
232 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 ...
