instruction_seed stringlengths 292 48.7k | found_ngrams listlengths 0 21 |
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Task
Here is an interesting math problem:
Let's say that there are \$n\$ indistinguishable unlabeled objects in a bin. For every "round", pull \$k\$ objects randomly out of the bin with equal probability, and apply a label on each object (Nothing happens to objects already having a label). Then put these \$k\$ objects... | [] |
We already have a challenge for polynomial interpolation: given a list of points, output the coefficients of the polynomial that passes through them.
Hermite interpolation is a generalization of polynomial interpolation. Instead of just specifying the points that the polynomial passes through, we also specify the highe... | [] |
We will think of a partition as a sequence of non-increasing integers.
For a given partition into \$n_1, n_2, \dots, n_k\$ with \$n_1 \geq n_2 \dots n_{k-1} \geq n_k = n\$ we write it out with \$n_i\$ dots on row \$i\$. So for \$6, 1, 1\$ we would write six dots on the first row, one on the second and one on the third... | [] |
Task
Your boss is on another crusade for 'efficiency.' He wants to encourage the use of numbers with fewer syllables, so that they're easier to discuss in meetings. If you want to take some time off work, you're boss would prefer you take 9 days instead of 7. You're boss would prefer a credit card expense of $99,502 ov... | [] |
Imagine there are \$n\$ people \$\{a_1, a_2, \ldots, a_n\}\$ who enter a room in order and sit down in \$n\$ seats, arranged in a row. Each of these people belong to some gang, indicated by an integer \$\{1, 2, \ldots, k\}\$. These gangs hate the members of the other gangs, so they want to sit as far away from those pe... | [
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The well-known Urinal Protocol states that each person that takes a urinal will take the one furthest from any other taken urinal. But this fails to account for short urinals; in many cases, a person would prioritize taking a taller urinal in addition to distance.
In the real world, you might struggle to find a restroo... | [] |
The Rudin-Shapiro sequence is a sequence of \$1\$s and \$-1\$s defined as follows: \$r_n = (-1)^{u_n}\$, where \$u_n\$ is the number of occurrences of (possibly overlapping) \$11\$ in the binary representation of \$n\$.
For example, \$r_{461} = -1\$, because \$461\$ in binary is \$111001101\$, which contains \$3\$ occu... | [] |
We need to produce a block cipher round function with a 1 bit round key size and a 7 bit message size with the highest level of cryptographic security according to our measure of security.
Introduction
We are going to need new symmetric encryption functions. We are at the point where we cannot improve the performance o... | [] |
One lane is closed, the vehicles have to thread their way in according to the zip-lock system: One car from one lane, the next car from the other lane, always taking turns.
Input: Two vehicle queues, represented e.g. as strings, in which short cars are represented by individual symbols, lorries by several identical sym... | [] |
It is a well-known fact that you can colour a two-dimensional map with four colours in such a way that two countries with a common border always have different colours. There have already been enough challenges on this topic.
However, the prerequisite for this is that there must be no enclaves, i.e. non-contiguous area... | [] |
Objective
Given two non-negative integers encoded in unbounded-length Gray code, add them and output the result, where the result is also encoded in Gray code.
Gray code
There are many equivalent formulations of Gray code, but here's an intuitive one.
The Gray code encodes each non-negative integer as an infinite bit-s... | [] |
Challenge
This challenge is based on the domino effect:
Initially, each domino is located on one straight line and is in a vertical state. It can be dropped either to the left along the same straight line, or to the right. Then this domino will knock down the next one, and that one, perhaps, the other.
The dominoes are... | [] |
Given a string of ASCII text as input, encode it in BPSK31 using Varicode. You may either output an audio file in any common format, or play the audio over the device speakers. You may output at any sample rate and with any carrier frequency between 500 Hz and 2500 Hz. The sample rate and carrier frequency must be cons... | [] |
You know what a monotonic sequence is: each element is bigger than its predecessor (monotonically rising) or as its successor (monotonically falling).
Bitonic means you have two arms of the sequence, one monotonically rising, the other falling.
For example, 1,3,5,7,6,4,2 is bitonic (rising until 7, then falling until t... | [] |
In this challenge, an infinitely proportional sequence is defined as a infinite sequence of positive integers such that:
All positive integers are contained infinitely many times within the sequence.
As more and more terms are added to the sequence, for all positive integers \$n\$, the ratio of the number of \$n\$s to... | [] |
OEIS sequence A003242 comprises the numbers of Carlitz compositions for any given positive integer. This is the number of integer partitions of the integer for which no two adjacent parts are equal.
For example, for 4:
Generate the possible integer partitions (and their permutations): [1,1,1,1], [1,1,2], [1,2,1], [2,1... | [] |
Given an n non-negative integers, how many numbers must be changed so that each number x appears x times? You cannot add or remove elements, only replace them with other numbers.
For example:
1 6 23 6 9 23 1 1 6
can be turned into:
1 6 2 6 6 2 6 6 6
with 5 changes, which is optimal.
Test cases
0 => 1
1 2 3 => 1
5 5 5... | [] |
Every Brazilian citizen has a national identification number associated with them, named CPF.
This number has 11 digits (formatted as XXX.XXX.XXX-XX) and it's validated by the following (real) algorithm1:
Take the 9 most significant digits of the number. Call it c.
Multiply the n-th least significant digit of c by n+1... | [
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I define mousetail's sequence as follows:
If the nth element of the sequence is q, then n+1 must appear q times in the sequence
The sequence is weakly monotonically increasing (i.e. no lower number may follow a higher number)
f(1)=1
I'll show an example of how this works:
the first element is 1
after the 1, come 1 2... | [] |
Historic Tetris Achievement
Blue Scuti became the first ever human to beat the classic game of Tetris on NES.
Here's the Tetris Kill Screen
Challenge
Output the following Tetris Kill Screen board (10x20 blocks)
EEEEEEEEEE
EEEEEEEEEE
EEEEEEEEEE
EEEEEEEEEE
EEEEEEEEEE
EEEEEEEEEE
EEEEEEEEEE
EEEEEEEEEE
EEEEEEEEEE
EEEEGGEEE... | [] |
Earlier I asked about this problem on stackoverflow (link), but now I also want to see the golfiest solutions
Problem:
Given an array of arbitrary numbers, what is the longest subarray that is repeated (appears more than once)? In case there are multiple distinct repeated subarrays that all have the longest length, the... | [
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20
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Consider a function \$r\$ where
$$
r(i,k)= \begin{cases}
L_{i+1}-L_i, & \text{if}\ k =0\ \text{ (1st reduction)} \\
r(i,0)-r(\lfloor \log_2{k} \rfloor,k-2^{\lfloor \log_2{k} \rfloor}) & \text{if}\ k \geq 1\ \text{ (2nd reduction)}
\end{cases}
$$
where \$k<2^i\$ and \$L\$ is a finite sequence of integers.
For example,... | [
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Definitions
The common methods to generate consecutive composites are
$$\overbrace{(n+1)! + 2, \ (n+1)! + 3, \ \ldots, \ (n+1)! + (n+1)}^{\text{n composites}}$$
$$\overbrace{n!+2,n!+3,...,n!+n}^{\text{n-1 composites}}$$
$$\overbrace{n\#+2,n\#+3,…n\#+n}^{\text{n-1 composites (Primorials)}}$$
A less common method involv... | [] |
Exposition
In this challenge, I am talking about ARM assembly language. ARM is a 32-bit RISC processor; I'll use instruction set up to architecture v6.
To load a constant ("immediate") value into a register, use
the MOV instruction:
MOV r8, #42
To load negative values, use the MVN instruction, with a bit-complement of... | [] |
Even though the concept of phat-fingered-lights-out number should be pretty self-explanatory here is a definition:
Given a nonnegative integer in binary representation a phat-fingered double-bit-flip or phatflip for short replaces a pair of adjacent, equal bits with their complement.
For example given the number 0b1110... | [] |
Input: You are given two numbers n and m.
Create the snail: Given an n >= 3, fill an n * n grid with the numbers from 1 to n * n, starting at the top left, going clockwise to the middle like this (for n = 5):
1 2 3 4 5
16 17 18 19 6
15 24 25 20 7
14 23 22 21 8
13 12 11 10 9
Calculate the sum of the neightbour... | [] |
Background
As noted in this question, for all positive integers \$n>2\$ there exists at least one Egyptian fraction representation (EFR) of \$n\$ distinct positive integers \$a_{1} < a_{2} < \dots < a_{n}\$ such that $$ \sum_{k=1}^{n} \frac{1}{a_{k}} = 1. \tag{1} \label{1} $$
When \$n=3\$, for instance, we have $$ \fra... | [] |
A list \$[a_1,a_2,a_3 \cdots a_n]\$ can be uniquely represented as an unordered list of its prefixes - \$ [[a_1],[a_1, a_2], [a_1,a_2,a_3] \cdots [a_1,a_2,a_3 \cdots a_n]] \$. This can be in any order - for example, \$[1, 2, 3]\$ could be represented by any of \$[[1],[1,2],[1,2,3]]\$, \$[[3,2,1],[2,1],[1]]\$, or \$[[2,... | [] |
Challenge
Given ASCII-encoded text input of any size, detect numbers between -1,000,000,000,000,000,000 and 1,000,000,000,000,000,000 exclusive and rewrite them with thousands separators. Use commas only and ignore leading zeroes. Leave the rest of the input unchanged.
Test cases
Input
Output
Description
123
123... | [] |
Given a collection of coloured laces, what would be the probability, \$P\$, that Alice won't create any loops if, until impossible, they tie two uniformly chosen, free lace ends of differing colours together?
For the avoidance of doubt:
Each lace will be of only one colour and will have precisely two ends.
Alice does ... | [] |
I recently found this game and have been enjoying it. Basically, there is a grid of colored tiles and you act by clicking on empty spaces. When you click an empty space, the first tile (if any) in each of the four axis-aligned directions is selected. If any color appears more than once, all tiles of that color are dest... | [] |
Given a non-empty sequence of non-negative integers, output any permutation of it in which no two adjacent elements have a sum that is divisible by 3. If it is impossible, either crash the program, return an empty sequence, or output nothing.
The asymptotic time complexity must be linear in the size of the input sequen... | [] |
All integers \$n > 0\$ can be expressed in the form
$$n = \prod_{\text{prime } p} p^e = 2^{e_2} 3^{e_3} 5^{e_5} 7^{e_7} \cdots$$
This form is also known as it's prime factorisation or prime decomposition, and each integer has a unique prime factorisation.
As the bases are fixed, it is possible to reconstruct an integer... | [] |
Background
For the purpose of this challenge, all numbers and their string representations are assumed to be in decimal (base 10). I tried to find proper terminology for this challenge, but I do not think there is any, so I made it up.
A self-replicating number is a number that appears as a substring in any of its mult... | [] |
The primorial \$p_n\#\$ is the product of the first \$n\$ primes. The sequence begins \$2, 6, 30, 210, 2310\$.
A Fortunate number, \$F_n\$, is the smallest integer \$m > 1\$ such that \$p_n\# + m\$ is prime. For example \$F_7 = 19\$ as:
$$p_7\# = 2\times3\times5\times7\times11\times13\times17 = 510510$$
Adding each num... | [] |
Create all arrays of non-negative integers of length N where the array sum is equal to T. The output order of arrays does not matter.
Possible solutions are e.g.
N = 5, T = 2:
1 1 0 0 0
1 0 1 0 0
1 0 0 1 0
1 0 0 0 1
0 1 1 0 0
0 1 0 1 0
0 1 0 0 1
0 0 1 1 0
0 0 1 0 1
0 0 0 1 1
2 0 0 0 0
0 2 0 0 0
0 0 2 0 0
0 ... | [] |
Related: Zeroes at the end of a factorial
Today, we are going to calculate how many zeroes are there at the end of \$n!\$ (the factorial of \$n\$) in base \$m\$.
Or in other words: For given integers \$n\$, and, \$m\$. Calculate the integer \$p\$ which is the highest power of \$m\$ dividing \$n!\$: \$p \in \mathbb{N}_0... | [] |
This fastest-code challenge is based partly on this MSE question and exists to extend some OEIS sequences, and create others. If I extend or create sequences based on this challenge, I'll link to this challenge so that folks can see where the values come from. If you'd like direct credit, include your first and last na... | [] |
In this code golf challenge, you'll be computing the placement of (open) circles of areas \$\pi, 2\pi, 3\pi, \dots\$ when greedily placed along integer points in a square spiral in such a way that no two overlap.
A square spiral is a sequence in \$\mathbb Z^2\$ that starts at \$(0,0)\$ and successively wraps around the... | [] |
Fibonacci coding is a universal code, which can encode positive integers of any size in an unambiguous stream of bits.
To encode an integer \$ n \$:
Find the largest Fibonacci number less than or equal to \$ n \$; subtract this number from \$ n \$, keeping track of the remainder
If the number subtracted was the \$ i \... | [] |
AND THE WINNER IS....
Command Master's "Ball Pulling"!
Note: Competition is over, but more submissions are welcome!
Ball game is a game I invented where two players start with 100 energy each. Every turn, each player independently chooses an amount of energy to spend. Whoever spends more energy brings the ball 1 uni... | [] |
Introduction
Note that I learned it from a Numberphile Video, where Neil Sloane explains it better. I recommend you to watch his Video. But for a quick Introduction:
The Levine Sequence is made from the Levine's Triangle, which is made as follows:
First you have \$0\$ ones, and \$1\$ twos.
Then you read the list back... | [] |
Ash has a bit of an interesting float division algorithm. It's designed to never return NaN, and things like signed zero and infinity need to be handled.
How it works:
Assume the inputs are positive for the rules below. One input being negative will always result in the output being negative, and both being negative wi... | [] |
Background
Flow Free is a series of puzzle games whose objective is to connect all the same-colored pairs of dots on the grid. Flow Free: Warps introduces the "warping" mechanic: a line connecting two dots can go through the border of the grid, which makes it re-enter through the opposite side of the grid (torus topolo... | [] |
Inspired by this question on Stackoverflow.
The task
Let's have two lists/arrays of integers: L1 and L2 of equal length. You need to identify in L2 the position of first occurrence of each number and remove from L1 the values on the corresponding positions. Then print/output the modified L1.
Any reasonable input/ouput... | [] |
An \$n\times n\$ Latin Square is a grid containing exactly \$n\$ distinct values where the values in each row and column are distinct. For example,
$$\begin{matrix}
A & B & C \\
C & A & B \\
B & C & A \\
\end{matrix}$$
is a Latin square as no row or column contains a repeated value.
You are to take a positive integer \... | [
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The age-old question - is it better to walk or run? There are two trains of thought. If you run, you cause the rain to effectively hit you from the front, which increases your surface area and basically causes you to run into the raindrops, getting hit with more water. However, if you walk, you spend longer in the rain... | [
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Given a list of positive digits, return that list with consecutive elements grouped together. For example:
[1, 2, 3, 5, 6, 5, 4, 4, 1] -> [[1, 2, 3], [5, 6, 5, 4], [4], [1]]
Essentially, all adjacent elements whose absolute difference is 1 should be grouped together.
The input array will only ever contain positive dig... | [
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],
[
220,
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220,
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220,
18,
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This challenge is inspired by the game No More Jockeys.
The input is a list of tuples of natural numbers (potentially including 0), in some appropriate input format. Starting with player 0 and alternating with player 1, each player chooses some number which is contained within at least one remaining tuple, and all tupl... | [] |
Given a list of non-negative integers, return whether or not that list is all the same number.
Rules
Input and output can be taken/given in any reasonable and convenient format
Truthy/Falsey values can be represented as any value of your choice as long as it's reasonable and relatively consistent (e.g. 1 for falsey an... | [] |
Gelatin is a worse version of Jelly. It is a tacit programming language that always takes a single integer argument and that has 7 (or maybe 16) commands. You are to take in a Gelatin program and its argument and output the result.
Gelatin
Gelatin programs will always match the following regex:
^[+_DSa\d~]*$
i.e. they... | [] |
a.k.a. You Can Output Anything With Labyrinth Or Hexagony™
Challenge
In a recent restricted-source challenge, I could print any character with only half of the allowed digits with very small character count, by abusing the "digit commands" and modulo-256 output function. Now, it's about time to make a general metagolfe... | [
[
16,
11,
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18,
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19,
11,
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20
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Bob has a startup that is developing a product that uses “advanced AI” and “black magic” to automatically code-golf computer programs. Unfortunately, Bob is running out of cash and desperately needs money from investors to keep his company running. Each investor that Bob has contacted wishes to schedule a meeting with ... | [] |
Introduction
In this TED-Ed video (which I'd recommend watching first), a puzzle is presented. 27 unit cubes must be painted with one of red, green, or purple on each face, so that they can be reassembled into a large 3x3x3 cube that shows only red on the outside, then a different arrangement that shows only green, and... | [] |
Gelatin is a worse version of Jelly. It is a tacit programming language that always takes a single integer argument and that has 7 (or maybe 16) commands.
Gelatin
Gelatin programs will always match the following regex:
^[+_DSa\d~]*$
i.e. they will only contain +_DSa0123456789~ characters. The commands in Gelatin are:
... | [] |
A challenge many developers face when drawing a graph from scratch to plot some data is generating its ticks. In below graph, there are 6 horizontal ticks (1750, 1800, 1830, 1860, 1880 and 1900) and 11 vertical ticks (0, 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100).
The horizontal bounds of the above graph goes from 17... | [] |
Background
The Collatz (or 3x+1) map (A006370) is defined as the following:
$$
a(n) =
\begin{cases}
n/2, & \text{if $n$ is even} \\
3n+1, & \text{if $n$ is odd}
\end{cases}
$$
Now, let's define the sequence \$s_0\$ as the infinite sequence of positive integers \$1, 2, 3, 4, \cdots\$, and define \$s_k\$ as the result... | [
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[
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18,
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Inspired by a discussion from the Esolangs.org unofficial Discord Server.
Instructions
A chess cycle is an arrangement of a chess board where each piece must attack one other piece, and only one other piece, and each piece is attacked exactly once.
The effective idea to to "connect" pieces with each other, forming a si... | [] |
Background
Inspired by this video by Matt Parker
A Faro shuffle is a perfect riffle shuffle where the deck is exactly interleaved with its other half. This is how to perform one:
the deck of 52 cards is split into two piles of 26 cards each
the two piles are interleaved. In the case of an "in" shuffle, the bottom card... | [
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Introduction
When playing Mario Kart the other day, an interesting question popped up when a Grand Prix with my 2 roommates, 9 AI drivers and myself seemed to be fairly close and therefore exciting until the very end.
We asked ourselves: How close can the point difference between first and last place (#1 and #12) after... | [] |
Lucky numbers (A000959) are numbers generated by applying the following sieve:
Begin with the list of natural numbers:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, ...
Now, remove every second element (\$n = 2\$, the smallest element in the list aside from 1):
1, 3, ... | [
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Given:
a blackbox function \$f : \mathbb N \to \mathbb N\$,
a list of positive integers \$L\$, and
a list of indices \$I\$,
apply \$f(x)\$ to the elements of \$L\$ at the indices specified in \$I\$.
For example, \$f(x) = x^2, L = [7, 6, 3, 9, 1, 5, 2, 8, 4]\$ and \$I = [3, 5, 8]\$ (using 1 indexing), we apply \$f(x)\... | [] |
Related: Calculate \$f^n(x)\$, Polynomialception
Challenge
Given a polynomial \$f(x) = a_0 + a_1 x + a_2 x^2 + \cdots + a_k x^k\$ of order \$k\$, we can compute its composition with itself \$f\left(f(x)\right) = f \circ f(x) =: f^2(x)\$, which evaluates to another polynomial of order \$k^2\$.
The challenge is to revers... | [] |
Inspired by this: http://nolandc.com/smalljs/mouse_reveal/ (source).
A valid answer:
Takes a number
\$w\$ and (assumed non-negative) integer \$x\$.
Starts with an integer list with a length of \$2^w\$, initially filled with zeroes.
For each number \$n\$ from \$0\$ to \$w-1\$ (inclusive), divides the list into sub-list... | [] |
Given a non-empty list of integers between 1 and 9 inclusive, find the longest contiguous sublist such that the number of occurrences of each element (of the sublist) within the sublist is equal (not the number of consecutive occurrences, just the total count). You may return any non-empty subset of the solutions.
Exam... | [] |
In this king-of-the-hill challenge, you will be making a python 3 bot to play the card game judgement!
Sandbox
Rules
Judgement is a hand based game similar to games like rummy. In each round,
7 cards are dealt to each player, a trump suit is chosen (trump suits are chosen sequentially from the list Spades/Hearts/Diamon... | [] |
An addition-subtraction chain, is a sequence \$a_1, a_2, a_3, ... ,a_n\$, such that \$a_1=1\$ and for all \$i > 1\$, there exist \$j,k<i\$ such that \$a_i = a_j \pm a_k\$.
Your task, is given a number \$x\$, find the shortest addition-subtraction chain, such that \$a_n = x\$.
Rules
You can assume the input is a valid ... | [] |
Do you know the optical effect of a tridimensional hand painted whit horizontal lines?
Examples
This challenge consists of making something like that effect with ascii, and transforming one 2d input into a "3d" output.
The algorithm
To perform this transformation, you first replace all 1 with a ¯ and all 0 with a _. In... | [] |
There is a boy named Peter. Peter is a picky eater and doesn't like to eat the same kind of cookie again on the same day.
Peter gets a present, The present is a box of cookies! The box contains \$K\$ types of cookies. Also, it contains different amount of each type of cookie.
Peter, being the picky eater he is, Wants t... | [] |
Introduction
Dr. Leslie Lamport, of the eponymous Lamport one-time signature scheme, is getting rather old. But he can't die until his most famous algorithm gets all the kinks ironed out!
In particular, that scheme had one internal component he was never satisfied with:
We hope that someone can find a more elegant met... | [
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[
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Background
Link-a-Pix is a puzzle on a rectangular grid, where the objective is to reveal the hidden pixel art by the following rules:
Connect two cells with number N with a line spanning N cells, so that the two cells are at the two ends of the line.
The number 1 is considered connected to itself (which makes it an e... | [] |
Task
Given a non-empty list of positive digits, group them into sublists of equal sum. You may output any subset of solutions with maximal number of sublists (equivalently, minimal sum).
The input may contain repeat elements. There may not exist any solution but the singleton list containing the input itself. The outpu... | [] |
Take this array:
[1, 2, 6, 4, 4, 1, 0, 0, 2, 0, 4, 1, 4, 2, 4, 8, 1, 2, 4]
There are quite a few places where [1, ..., 2, ..., 4] appears, where ... is any number of items. These include [1, 2, 6, 4], [1, 0, 0, 2, 0, 4], [1, 0, 0, 2, 0, 4, 1, 4], and [1, 2, 4]. The shortest of these is simply [1, 2, 4].
Task:
Given t... | [] |
Inspired by this Numberphile video.
What is planing?
In order to 'plane' a sequence of digits, you need to:
Identify the lengths of the 'runs' (adjacently repeated digits) in the sequence. Non-repeated digits count as runs of one.
Decrease the length of each run by one. Runs of length 1 become length 0.
Reconstruct t... | [] |
If you convert a chemical formula to lower case, it may become ambiguous: co can be both CO or Co.
Given an input consisting of a-z0-9, where 0 can only stand behind 0-9. Check whether it's ambiguous, unambiguous, or impossible. Return 3 different values for them. Shortest code wins.
Examples:
co - ambiguous
2h83o6... | [] |
Program the sequence \$R_k\$: all numbers that are sum of square roots of some(maybe one) natural numbers \$\left\{\sum_{i\in A}\sqrt i\middle|A\subset \mathbb{N}\right\}\$, in ascending order without duplication. Outputting zero is optional.
You should do one of:
Take an index k and output \$R_k\$, either 0 or 1 inde... | [] |
Given an integer \$1 < n < 10 \$ generate a table like below.
For \$n = 5\$,
1 2 3 4 5
2 2 3 4 5
3 3 3 4 5
4 4 4 4 5
5 5 5 5 5
For \$n = 8\$,
1 2 3 4 5 6 7 8
2 2 3 4 5 6 7 8
3 3 3 4 5 6 7 8
4 4 4 4 5 6 7 8
5 5 5 5 5 6 7 8
6 6 6 6 6 6 7 8
7 7 7 7 7 7 7 8
8 8 8 8 8 8 8 8
Shortest code wins! Trailing whitespace allowed
... | [] |
But Is It Art? is an esolang created by ais523, where one step is break the program into orthogonally connected "tiles":
A BBBB
A B B
AA CC
A CC
Each separate letter shows a different tile. Interestingly, programs in But Is It Art? only rely on the orientations of the tiles themselves, not their placement. This means... | [] |
Multi-dimensional chess is an extension of normal chess that is played on an 8x8x8x8... "board".
In normal 2D chess, a knight's move is a movement by a vector of \$ \begin{bmatrix} \pm 2 \\ \pm 1 \end{bmatrix} \$ or \$ \begin{bmatrix} \pm 1 \\ \pm 2 \end{bmatrix} \$, as long as it doesn't cause the knight to go outside... | [] |
Mr. Binary Counterman, son of Mr. Boolean Masker & Mrs. Even Oddify, follows in his parents’ footsteps and has a peculiar way of keeping track of the digits.
When given a list of booleans, he counts the 1s and 0s separately, numbering the 1s with the odds & the 0s with the evens.
For example, when he looks at 1 1 0 0 1... | [] |
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_{k=0}^{n}{(-1)^k \binom{n}{k} a_k}$$
It has an interesting property that applying the transform twice will yield the ori... | [
[
16,
11,
220,
17,
11,
220,
18,
11,
220,
19,
11,
220,
20
],
[
16,
11,
220,
16,
11,
220,
17,
11,
220,
18,
11,
220,
20
],
[
11,
220,
17,
11,
220,
18,
11,
220,
19,
11,... |
Your challenge is to write a function/program that takes a matrix of integers m and a number n as input and:
Splits m into n by n chunks
Replaces each chunk with the most common value in that chunk (In case of a tie, any of the tied values is fine).
Outputs the resulting matrix.
Note: You can take either the size ... | [] |
Inspired by Wzl
Determine if a given square binary matrix has exactly one row or column consisting of entirely 1s, and the rest of the matrix is 0s.
For example, these are all true:
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1
0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ... | [] |
In November 2019, Alon Ran published a particularly lovely sequence in the OEIS, A329126:
\$a(n)\$ is the lexicographically earliest string of digits which yields a multiple of \$n\$ when read in any numeric base.
1, 110, 101010, 111100, 100010001000100010, 1111110, 10000010000010000010000010000010000010, 11111111000,... | [] |
Background
Minkowski addition is a binary operation on two sets of points (usually geometric objects) in the Euclidean space. The Minkowski sum of two sets \$A\$ and \$B\$ is formally defined as follows:
$$ A+B = \{\mathbf{a}+\mathbf{b}\,|\,\mathbf{a} \in A,\ \mathbf{b} \in B\} $$
To say in plain English, given the ori... | [] |
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 difficult to store this factorisation in a small manner. Being primes, we can't then factorise them, but we can factorise... | [] |
Input a non-empty array with \$n\$ positive integers. Test if the input array contains every integer in \$1\cdots n\$.
In case you prefer 0-indexed numbers, you may choose to input an array of non-negative integers, and test if the input array contains every integer in \$0\cdots (n-1)\$ instead. All testcases and formu... | [] |
Given an array \$A\$ of size \$n\$.
You have to find the number of subsets such that their product is in the form of \$p_1 \times p_2 \times p_3 \dots\$
where \$p_1, p_2, p_3, \dots\$ are prime numbers. No prime number should appear more than once, i.e. the product is "squarefree".
Example:
Lets pick an array \$A\$ of ... | [] |
As some of you may remember, Peter, who was a picky eater is now puzzled Peter.
This time Peter got some puzzles as a present from his Aunt. He has tried a lot, but has failed to solve the puzzles. Peter needs your help to solve them.
Each one of the puzzle has 2 pieces. To solve the puzzle, you must tell the number of... | [] |
Totally not inspired by Lyxal repeatedly mentioning elevators in chat :P
Challenge
In short: simulate some people filling up an elevator and then leaving it.
The elevator is simplified as a grid, where each person can occupy one cell of the grid. The height and width of the grid is the input parameter. The width is alw... | [] |
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 198539 (here it's 9).
For any given uniformly random string of \$N\$ digits in the set \$\{0,1,2,3,4,5,6,7,8,9\}\$, what is... | [] |
A complete Boolean function is a function such that, an amount of them can be used to express any Boolean function. For example, NAND \$\left[\begin{matrix}\text{input1}&0&0&1&1\\\text{input2}&0&1&0&1\\\text{output}&1&1&1&0\end{matrix}\right]\$ is complete. Inputs may be reused any number of times, and the functions ca... | [] |
I'd like to roll up the ability scores for my Dungeons and Dragons character. But I'd also like them to be balanced (and slightly better than average).
Typically, a character's stats are created by rolling four 6-sided dice, adding together the three highest results, and doing this 6 times. A 6 sided die has the number... | [] |
This challenge was inspired by this tweet.
Idea
Consider a circle with n evenly spaced dots around the perimeter, where each dot has a postive integer value:
Now connect the dots with non-intersecting chords:
Next consider our score, which is the sum of the products of these pairs. When n is odd, the extra orphan do... | [
[
16,
11,
220,
17,
11,
220,
18,
11,
220,
19,
11,
220,
20
],
[
11,
220,
17,
11,
220,
18,
11,
220,
19,
11,
220,
20,
11
]
] |
Challenge
Given a graph (a structure consisting of nodes and vertices), classify it according to a few categories.
Specifically, you will be given an unweighted directed graph, which is a set of nodes and edges from one node to another (but not necessarily both ways). You can take this in any reasonable and consistent ... | [] |
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)
$$
The Torian is then equal to \$x!x\$ for a given \$x\$. This sequence begins \$0, 1, 2, 24, 331776, ...\$ for \$x = 0, 1, 2, 3, 4, ...\$
Al... | [] |
Related: What's my telephone number? which asks to calculate the terms of A000085, the number of possible ordinal transforms of length n.
Background
Ordinal transform is a transformation on an integer sequence. For a sequence \$a=(a_0, a_1, a_2, \cdots)\$, the \$n\$-th term of the ordinal transform \$ord(a)_n\$ is defi... | [
[
16,
11,
220,
17,
11,
220,
18,
11,
220,
19,
11,
220,
20
],
[
11,
220,
17,
11,
220,
18,
11,
220,
19,
11,
220,
20,
11
],
[
220,
16,
11,
220,
17,
11,
220,
18,
11,
220... |
A screen consisted of some LED segments like such:
_ _ _ _ _
|_|_|..._|_|_|
|_|_| _|_|_|
However, some of the LEDs are broken, and it's possible that only these are left:
_ _
_|_|
|_|_|
Now, you're required to output all integers possibly expressed on this screen. An integer, something matching RegEx /^0$|^-?... | [] |
Given an array of integers. Find out its longest sub-array (contiguous subsequence) whose sum is 0.
The sub-array for output may be an empty array.
Input
Input an array of integers.
Output
Output the longest zero sum sub-array. If there are multiple such arrays, output any one of them.
Output Format
You may output in o... | [] |
Background
A Jordan matrix is a block-diagonal matrix where each block on the diagonal has the structure of
$$
\begin{bmatrix}
\lambda & 1 & 0 & \cdots & 0 \\
0 & \lambda & 1 & \cdots & 0 \\
\vdots & \vdots & \vdots & \ddots & \vdots \\
0 & 0 & 0 & \lambda & 1 \\
0 ... | [] |
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