Questions tagged [math]
The challenge involves mathematics in some central way. Also consider using more specific tags, listed in the tag wiki info.
1,599
questions
16
votes
21answers
2k views
Digit small numbers
A digit small number is a positive integer \$n\$ such for any two numbers that multiply to \$n\$, their total number of digits is more than the digits in \$n\$.
In otherwords: there are no two ...
23
votes
11answers
1k views
Infinite ordinals from a well-ordering
Your task is to write a short program that represents a large (infinite) ordinal, using a well-ordering of the set of positive integers. Your program will take two different positive integers and ...
1
vote
2answers
99 views
When the result will reach the people? [closed]
Assume the result of an exam has been published.
After 5 minutes, First person knows the result.
In next 5 minutes, new 8 persons know the result, and in total 9 know it.
Again after 5 minutes, new 27 ...
11
votes
9answers
966 views
Bijective meets mixed base
Background
A bijective base \$b\$ numeration, where \$b\$ is a positive integer, is a bijective positional notation that makes use of \$b\$ symbols with associated values of \$1,2,\cdots,b\$.
...
13
votes
19answers
1k views
Find the k-th order summary of a number
Background
The summary of a non-negative integer \$n\$ is the concatenation of all digits that appear in \$n\$ in increasing order, with each digit being preceded by the number of times it appears in \...
7
votes
27answers
2k views
How long is the number in this base?
Given a positive integer \$n\$ and another positive integer \$b\$ (\$1 < b < 36\$), return the number of digits/length of \$n\$ in base \$b\$
...
20
votes
9answers
2k views
Bird's Algorithm for Computing Determinants
There is a division-free algorithm for computing determinants published by R.S.Bird in 2011 that uses only matrix multiplications. Given a \$n×n\$ matrix \$X\$, the matrix \$Y=μ(X)\$ is another \$n×n\$...
1
vote
0answers
78 views
Make me equal to 24 [duplicate]
Based on this game.
Description :
Based on Wikipedia's description.
The 24 Game is an arithmetical card game in which the objective is to find a way to manipulate four integers so that the end result ...
6
votes
4answers
567 views
Solve linear equations over the integers
All variables in this question are integer valued.
Input
4 integers w, x, y, z. They can be positive or negative and will be less than 1048576 in absolute value.
Output
The general solution to the ...
10
votes
7answers
1k views
Fibonacci-like gap formula
Background
The recurrence of the Fibonacci sequence is defined as
$$
f(n+2) = f(n+1) + f(n)
$$
From this recurrence alone, the following gap formulae (recurrences relating three terms with certain ...
14
votes
14answers
2k views
Inverse n-bonacci sequence
We all know about the Fibonacci sequence. We start with two 1s and keep getting the next element with the sum of previous two elements.
n-bonacci sequence can be defined in similar way, we start with <...
13
votes
13answers
2k views
Find the smallest solution for this simple equation
Input
4 integers w, x, y, z from the range -999 to 999 inclusive where none of the values is 0.
Output
4 integers a, b, c, d so that aw + bx + cy + dz == 0 where none of the values is 0.
Restrictions
...
20
votes
9answers
1k views
Self-referential triangle sequence
Output the flattened version of the sequence A297359, which starts like the following:
...
13
votes
7answers
3k views
Make S + S + ... + S as Large as Possible!
Let \$S \subset \mathbb N_{\geq0}\$ be a subset of the nonnegative integers, and let $$
S^{(k)} = \underbrace{S + S + \dots + S}_{k\ \textrm{times}} = \{ a_1 + a_2 + \dots + a_k : a_i \in S\}.
$$
For ...
17
votes
12answers
1k views
How many values of this type?
Background
The number of values for a given type is called the cardinality of that type, and that of type T is written as |T|.
Haskell and a few other languages ...
16
votes
1answer
583 views
Lean golf: Pascal vs. Fibonacci
The Pascal's triangle and the Fibonacci sequence have an interesting connection:
Source: Math is Fun - Pascal's triangle
Your job is to prove this property in Lean theorem prover (Lean 3 + mathlib). ...
21
votes
2answers
2k views
∀ a b. a + b = b + a
This question is a part of the lean LotM.
A ring is a type of structure that takes the rules of addition and multiplication we are familiar with and abstracts them, so we can reason about them. To do ...
17
votes
13answers
2k views
The Area of Rectangles
Getting the area covered by a rectangle is really easy; just multiply its height by its width. However in this challenge we will be getting the area covered by multiple rectangles. This is equally ...
16
votes
46answers
3k views
Implement the hyperfactorial
The objective
Given the non-negative integer \$n\$, output the value of the hyperfactorial \$H(n)\$. You don't have to worry about outputs exceeding your language's integer limit.
Background
The ...
2
votes
6answers
539 views
Multiplication for geometric algebra
The basis vectors for geometric algebra are
$$(e_0=1), e_1, e_2,\dots,e_n$$
They all square to 1 (we do not consider vectors which square to -1 or zero)
$$e_i \cdot e_i = 1$$
They are associative and ...
1
vote
0answers
165 views
Pythagoras' Golfing Grid [closed]
Recently, I created a binary word search that got me working with grids. It was fun, so I wanted to create some more similar content. Meet Pythagoras' Golfing grid:
Each of ...
4
votes
16answers
796 views
Written Word Equation
Word equations, but not as you know it! Given a sentence which will include two numbers, numerically, and a spelt operator, in the order seen in the examples, your goal is to give the numerical answer
...
3
votes
7answers
708 views
Yet another coin flipping problem
Problem
Starting with a set of 10 coins at the start where all coins are tails up, and given n number of integers \$x_1, x_2, x_3... x_n\$ representing n rounds of coin flipping.
At each round, we ...
19
votes
12answers
1k views
Minimally prepend numbers to get a symmetric Young diagram
Background
A Young diagram is a diagram that represents a nonincreasing sequence of positive integers using left-justified rows of squares. As an example, 5, 4, 1 ...
10
votes
16answers
666 views
Generate all \$3\times 3\$ magic squares
Though challenges involving magic squares abound on this site, none I can find so far ask the golfer to print / output all normal magic squares of a certain size. To be clear, a normal magic square of ...
11
votes
8answers
926 views
Boustrophedon transform
Related: Boustrophedonise, Output the Euler Numbers (Maybe a new golfing opportunity?)
Background
Boustrophedon transform (OEIS Wiki) is a kind of transformation on integer sequences. Given a sequence ...
12
votes
2answers
481 views
Is this an interval graph?
Background
An interval graph (Wikipedia, MathWorld, GraphClasses) is an undirected graph derived from a set of intervals on a line. Each vertex represents an interval, and an edge is present between ...
14
votes
3answers
230 views
Bijection between \$ \mathbb N \$ and at-most-\$n\$-ary trees
Background
Related: a golflang theory I posted in TNB a while ago
At-most-\$n\$-ary trees are rooted trees where each internal node has between 1 and \$n\$ children (inclusive). Two trees are ...
12
votes
4answers
551 views
Maximal hexagonal dot pattern
Challenge
Imagine a hexagonal grid as shown below. Let's call such a grid has size \$n\$ if it has \$n\$ dots on one side. The following is one of size 3:
...
9
votes
1answer
252 views
Flatten a parabola keeping the distances between points along the curve constant
Background
Math SE's HNQ How to straighten a parabola? has 4,000+ views, ~60 up votes, 16 bookmarks and six answers so far and has a related companion HNQ in Mathematica SE How to straighten a curve? ...
5
votes
5answers
215 views
Potential nonzero entries in an irregular sequence
Background
A338268 is a sequence related to a challenge by Peter Kagey. It defines a two-parameter function \$T(n,k)\$, which counts the number of integer sequences \$b_1, \cdots, b_t\$ where \$b_1 + \...
15
votes
19answers
1k views
Compare positions of integers in this sequence
A001057 is one way to represent an integer as a natural number. It lists them according to the following pattern:
0, 1, -1, 2, -2, 3, -3, 4, -4, ...
In this ...
9
votes
20answers
2k views
Third Stirling numbers of the second kind
\$\left\{ n \atop k \right\}\$ or \$S(n, k)\$ is a way of referring to the Stirling numbers of the second kind, the number of ways to partition a set of \$n\$ items into \$k\$ non-empty subsets. For ...
8
votes
4answers
314 views
Hexagonal section numbers
Introduction
Let's draw some regular hexagons formed by hexagonal tiles, marking the vertices of the tiles with dots. Then we will count the number of dots.
...
19
votes
7answers
2k views
Is this a Jordan matrix?
Background
A Jordan matrix is a block-diagonal matrix where each block on the diagonal has the structure of
$$
\begin{bmatrix}
\lambda & 1 & 0 & \cdots & 0 \\
0 &...
5
votes
3answers
149 views
Is this an ordinal transform? [duplicate]
Related: What's my telephone number? which asks to calculate the terms of A000085, the number of possible ordinal transforms of length n.
Background
Ordinal transform is a transformation on an integer ...
19
votes
21answers
2k views
Implement the Torian
The Torian, \$x!x\$, of a non-negative integer \$x\$ can be recursively defined as
$$
x!0 = x \\
x!n = \prod^x_{i=1} i!(n-1) = 1!(n-1) \times 2!(n-1) \times \cdots \times x!(n-1)
$$
The Torian is then ...
9
votes
2answers
322 views
Greatest Common Gaussian Divisor
Gaussian integers are complex numbers \$x+yi\$ such that \$x\$ and \$y\$ are both integers, and \$i^2 = -1\$. The norm of a Gaussian integer \$N(x+yi)\$ is defined as \$x^2 + y^2 = |x+yi|^2\$. It is ...
12
votes
2answers
272 views
Number of distinct shadow transforms
Background
Shadow transform of a 0-based integer sequence \$a(n)\$ is another 0-based integer sequence \$s(n)\$ defined with the following equation:
$$
s(n) = \sum_{i=0}^{n-1}{(1 \text{ if } n \text{ ...
1
vote
4answers
192 views
Chasing the car [closed]
Imagine you are sitting at a park. Suddenly your car gets hijacked and being driven in different directions. Here are the directions, arrows show which direction goes towards where:
...
15
votes
9answers
529 views
To raise \$ e \$ to the power of a matrix
Inspired by this 3Blue1Brown video
Given a square matrix \$ M \$, compute its matrix exponential \$ \exp(M) \$, which is defined, using an extension of the Maclaurin series for \$ e^x \$, as
$$ \exp(M)...
5
votes
10answers
1k views
Odds that a string of N digits contains two or more of the same
I have to fill in 2fa codes all day. They're 6-digit strings. One day I noticed that not once did any of these codes contain 6 unique digits, like 198532 There was always at least one double, like ...
6
votes
10answers
3k views
The worst ever phone number entry screen
The name of the challenge was prompted by this GIF and the GIF also gave me the idea.
Your challenge today is to take a input guaranteed to be \$2<=n<=100\$ and output a sequence of ...
22
votes
14answers
2k views
Find the Erdős–Woods origin
Consider, for a given positive integer \$k\$, the sequence \$(a, a+1, a+2, ..., a+k)\$, where \$a\$ is some positive integer. Is there ever a pair \$a, k\$ such that for each element \$a+i\$ in the ...
-5
votes
7answers
220 views
Take the numbers 1 to 100, square them, and add all the even numbers while subtracting the odd ones [closed]
Description
The task is simple enough:
Take the numbers 1 to 100, square them, and add all the even numbers while subtracting the odd ones.
It is taken from this blog post:
R Coding Challenge: 7 (+1) ...
17
votes
16answers
1k views
Reconstruct a recursively prime-encoded integer
Recursively prime-encoded integers
Consider \$11681169775023850 = 2 \times 5 \times 5 \times 42239 \times 5530987843\$. This isn't a nice prime factorisation, as \$42239\$ and \$5530987843\$ make it ...
8
votes
13answers
1k views
ASCII-Plot the equation
You are given a polynomial function, in the following format:
\$x = (c_0 * y^0) + (c_1 * y^1) + (c_2 * y^2) + ... + (c_n * y^n)\$
where \$c_n\$ stands for the coefficient of the \$n^{th}\$ power of \$...
10
votes
3answers
215 views
Minkowski sum of two convex polygons
Background
Minkowski addition is a binary operation on two sets of points (usually geometric objects) in the Euclidean space. The Minkowski sum of two sets \$A\$ and \$B\$ is formally defined as ...
18
votes
21answers
940 views
Binomial transform
Background
Binomial transform is a transform on a finite or infinite integer sequence, which yields another integer sequence. The binomial transform of a sequence \$\{a_n\}\$ is given by
$$s_n = \sum_{...
19
votes
1answer
537 views
Demonstrate some advanced abstract algebra
Consider a binary operator \$*\$ that operates on a set \$S\$. For simplicity's sake, we'll assume that \$*\$ is closed, meaning that its inputs and outputs are always members of \$S\$. This means ...