Questions tagged [math]
The challenge involves mathematics. Also consider using more specific tags: [number] [number-theory] [arithmetic] [combinatorics] [graph-theory] [geometry] [abstract-algebra].
1,340
questions
5
votes
1answer
323 views
+50
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 ...
16
votes
10answers
353 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 \$...
1
vote
0answers
46 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 ...
16
votes
18answers
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 ...
14
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 ...
10
votes
4answers
1k 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
497 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 ...
9
votes
1answer
244 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 ...
13
votes
0answers
362 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 ...
11
votes
5answers
593 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 \$...
15
votes
1answer
243 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 ...
asked Dec 13 '19 at 17:35
Post Rock Garf Hunter
54.8k12 gold badges178 silver badges395 bronze badges
28
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
299 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,...
15
votes
16answers
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 ...
17
votes
2answers
625 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\$ ...
33
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....
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
501 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 ...
2
votes
1answer
125 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
980 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
228 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
60answers
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
341 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
362 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
127 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
320 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
476 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 ...
38
votes
53answers
8k 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
777 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
714 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
382 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
466 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
301 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 ...
