Questions tagged [arithmetic]
Challenges related to elementary arithmetic.
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Palindromic Powers
Powers
We define an important power as a number that can be represented as \$ x^y \$ where \$ x ≥ 2 \$ and \$ y ≥ 2 \$.
Palindrome
We define an ...
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Random Point from a 2D Donut Distribution
A donut distribution (for lack of a better term) is a random distribution of points in a 2-dimensional plane, forming a donut-like shape. The distribution is defined by two parameters: the radius <...
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No parentheses shall be omitted
This expression actually has an omitted pair of parentheses.
1 + 2 * 3
To make things clear, it should be,
1 + (2 * 3)
Even ...
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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 ...
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Khinchin's constant bad estimate [closed]
Inspired by How to write down numbers having an infinity of decimals? Link 🇫🇷
Background
From Wikipedia: for almost all real numbers \$x\$, coefficients \$a_i\$ ...
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Hunt for discount
Story
My local pizza delivery introduced new discount. You get 50% discount from every second item on your order.
But being greedy capitalists, they forgot to mention that they will rearrange items ...
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Rows of the Collatz tree
Consider a binary tree built the following way:
The root node is \$1\$
For a given node \$n\$:
If \$n\$ is odd, its only child is \$2n\$
If \$n\$ is even, one of its children is \$2n\$. If \$\frac {...
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Calculate the integer square root of a matrix
Let \$A\$ be a square matrix that is at least \$2 \times 2\$ where each element is an integer. \$A^2 = A \times A\$ will then have the same dimensions as \$A\$, and will have integer elements. For ...
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Index and return 3 characters
The challenge is simple: Read 3 letters from a system input¹ and convert them to numbers (A-1, B-2, C-3...Z-26)². Print each of those numbers in the order the ...
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Blinking Lighthouses – Founder's Day Upgrade
To celebrate the island's next Founder's Day, colored filters (fuchsia, chartreuse, and aquamarine*) have been installed in every lighthouse. All lighthouses begin operation with their fuchsia filter,...
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Blinking Lighthouses
Lighthouses on an island have blink codes that let ships know which lighthouse they are seeing. Input should be strings of S and L. Here is a (Python) example of codes for 4 lighthouses as a list of ...
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Maximum number of squares touched by a line segment
Consider a square grid on the plane, with unit spacing. A line segment of integer length \$L\$ is dropped at an arbitrary position with arbitrary orientation. The segment is said to "touch" ...
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Ploughed fields via moduli
Let \$R, C\$ be positive integers and let \$0 < s \leq 1\$. Consider the \$R \times C\$ matrix \$\mathbf M\$ defined as
\begin{equation}
M(i,j) = \frac{\mathrm{mod}\,(j, i^s)}{R^s}, \quad i = 1, \...
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Crack the Lost Numbers
The Lost Numbers are 4, 8, 15, 16, 23, 42. Your goal is to create an expression to output them all.
Your allowed characters are 0123456789, ^+-*/, (), % for modulo and n as the single variable allowed....
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Distribute the additions!
Challenge: Given an expressions made of additions and multiplications, output an expression that is a sum of products. The output must be equivalent to the input modulo the law of distribution. For ...
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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 ...
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Collatz's ice cream cone factory
The Collatz sequence
Given a positive integer \$a_1\$, the Collatz sequence with starting value \$a_1\$ is defined as
\begin{equation}
a_{n+1} =
\begin{cases}
a_n/2 & \mathrm{if}\ a_n\ \mathrm{is}\...
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Make a "proof" generator
Introduction
How to prove that 1 = 2:
1 = 2
2 = 4 (*2)
-1 = 1 (-3)
1 = 1 (^2)
You can just multiply both sides by 0, but that's cheating. This is just bending the ...
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Inserting digits to satisfy equation
You are given 3 non negative numbers: \$x\$, \$y\$ and \$z\$, and must minimize the number of digits (non negative) inserted at any place in the numbers \$x\$, \$y\$, or \$z\$ to make
$$x + y = z$$
(a ...
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Exciting Mario Kart Grand Prix - Minimize the point difference!
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 ...
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Sum over an Interval [duplicate]
Inspired by this challenge, and similar to this and this.
After seeing these, I figured I would continue the trend as there was no inclusive/exclusive sum.
The goal here is to sum an interval of ...
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Implement ΔList [duplicate]
Given a list of integers, such as {1, 4, 2, 8, 10}, TI-Basic's ΔList will determine the difference between every overlapping ...
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Number of coins needed to make change
Relatable scenario: I'm going to the store to buy a single item, but only have a $100k bill. As a result, I need exactly $99,979 in change, and in the fewest coins/bills possible because I'm quite ...
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Multiplicative Persistence #2
We had a challenge on Multiplicative Persistence here.
As a recap, to get a multiplicative persistence of a number, do these steps:
Multiply all the digits of a number (in base \$10\$)
Repeat Step 1 ...
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Verify the inequality!
Left in sandbox for at least 3 days.
I want to verify if this inequality is true:
for \$n\geq4\$, if \$a_1,a_2,a_3,\dots,a_n\in R_+\cup\{0\}\$ and \$\sum_{i=1}^na_i=1\$, then \$a_1a_2+a_2a_3+a_3a_4+\...
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Next to the middle
Given an array of integers, find "the next to the middle".
The next to the middle is the smallest integer greater than the smallest among mean, median and mode of the given numbers, that is ...
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8 out of 10 programmers like countdown [duplicate]
Edit (Jan 24/2021): The original specification for the challenge had a few problems. Underneath the original text, I have added alternate conditions that were suggested by @caird-coinheringaahing (...
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increment a binary number without arithmetic manipulations [closed]
Input: binary string
Output: binary string that represents the binary input + 1
Example: Given 10111 as an input, output 11000
...
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Ken Iverson’s Favourite APL Expression?
Ken Iverson, 1920–2020
Let's implement his favourite expression:
Given a row of Pascal's triangle, compute the next row.
This can for example be computed by taking the input padded with a zero on the ...
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Multiply or Divide by n
Here's a simple challenge, so hopefully lots of languages will be able to participate.
Given a positive integer \$n\$, output \$A076039(n)\$ from the OEIS.
That is, start with \$a(1)=1\$. Then for \$n&...
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Square root of a base 10 positive integer, digit by digit [closed]
It is possible (Wikipedia reference) to compute the square root of any number in a digit by digit fashion using a simple (I had learned it in primary school) algorithm.
Challenge:
read a positive ...
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We're much closer than you think
Martin Ender's 2D programming language Alice has two different modes depending on what orientation the IP has: orthogonal (Cardinal mode) or diagonal (Ordinal mode). Commands in Alice change their ...
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Shortest "arithmetic" formula to output 1000 primes
Write a formula using only the digits 0-9, +, *, -, <...
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Concatenations of powers and their squares
At time of writing, my reputation is \$16,256\$. As I noted in chat,
Oh cool my rep is the concatenation of two powers of 2: 16,256
Or even the concatenation of a power of 2 and its square, which is ...
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The vanilla factorial challenge
Task
Given a non-negative integer \$n\$, evaluate the factorial \$n!\$.
The factorial is defined as follows:
$$
n!=\begin{cases}1 & n=0\\n\times(n-1)!&n>0\end{cases}
$$
Rules
All default I/...
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Find your dog's age
Task
Take the (integer) number of human years that the dog has lived, \$n\$, as input and return its age in dog years, \$d\$, to two decimal places.
The number of human years, \$n\$, will be between \$...
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Slowing Down Sped Up Videos
Summary
Videos which are sped up every time a particular word is said exist for everything from the Bee Movie to the classic Rick Roll. The goal for this challenge is to figure out how much you'd have ...
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Sum the array times n, except the last
I've been posting relatively hard challenges recently, so here goes an easy one.
Task
Given an array \$A\$ and a number \$n\$, calculate the sum of all numbers of \$A\$ multiplied by \$n\$, except the ...
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Compute xkcd's Wrong Times Table
The 2020-05-29 xkcd comic showed us the numbers that Randall Munroe feels would be most likely to result from multiplication, other than the correct answers. The table does seem to have some sort of ...
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Check if an array (or equivalent) has the same number of odd and even numbers - Code Golf Edition!
Inspired by this code review question, I am curious to see what happens if we turn that into a code-golf challenge!
The description is easy, the input is an array or any similar data structure with ...
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Perfect scores in Martian rules football
Story
Martians have been observing Aussie rules football matches from space with great curiosity. Having totally fallen in love with the game, they have been inspired to start their very own football ...
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How to find the original value based on modulus/reminder and some other information [closed]
This might be a very basic question in terms of math,
x % constant = x_modulus
(x + some_number) % constant = y_modulus
Given the value of ...
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Multiplication algorithm on a 4004
So I was playing around with this emulator of the Intel 4004 and decided I wanted to set a challenge for myself. The first use for the 4004 was in a calculator, so I decided that I would try to code ...
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Generate A065825
(This is A065825.) The sequence defaults apply, so you can pick another format other than this one.
Given an input integer n, find the smallest number ...
user92069
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Euler's Geometry Puzzle
Today (or tomorrow, depending on your timezone, by the time of posting) is the birthday of the great mathematician and physicist Leonhard Euler. To celebrate his birthday, this challenge is about one ...
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Boil eggs using hourglasses
These are the classical puzzles:
You need to boil eggs for exactly 9 minutes, or else the visiting Duchess will complain, and you will lose your job as head chef.
But you have only 2 Hourglasses, one ...
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(RGS 4/5) Inverting matrices modulo m
Task
Given an integer matrix M and a modulus m, find an inverse of M modulo ...
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(RGS 1/5) Binary multiples
A binary multiple of a positive integer k is a positive integer n such that n is written ...
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Shift the digits [closed]
Here, x (supplied as input) and n (the result of your computation) are both positive integers. n * x = n shifted. Find n.
Here's an example of shifting:
...
user92069