Questions tagged [arithmetic]
Challenges related to elementary arithmetic.
541
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American odds to probabilities
American odds (aka moneyline odds) are numbers like \$+150\$ or \$-400\$ used to express how much a winning bet would pay out. Convert odds to a fair win probability like this:
Positive odds \$+n\$ ...
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Otteretto Classic game scoring method
Brief description of the game
In the game Otteretto Classic (which you can test directly in your browser; try it!) the player has to form palindromic sequences using adjacent cells on a square grid. ...
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Compare Two Fractions With ASCII Art
Challenge
Write a program or function that takes in 4 non-negative integers, A, B, C, and D, that represent two fractions, A/B and C/D, where B and D are non-zero and A <= B and C <= D.
Output ...
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Given 4 fence lengths, what's the largest rectangular yard you can make?
Here's a very simple little problem that I don't believe has been asked before.
Challenge
Write a program or a function that takes in four positive integers that represents the lengths of movable but ...
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Add two real numbers ... probably
The problem statement here is pretty simple, take two real numbers on the range [0,1) as input and output their sum, with probability 1.
The catch here is that there are a lot of real numbers. There ...
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Summing the Digits of a Number
Challenge
Given a non-negative integer, find the sum of its digits.
Rules
Your program must take a non-negative integer as input.
Your program should output the sum of the digits of the input ...
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Parse basic arithmetic into an AST
Introduction
An abstract syntax tree (AST) is a tree of tokens that shows their connection to each other and syntactical meaning. They are commonly used in compilers and static analysis tools, as ...
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Division between two strings
Inverse function of this challenge
To (properly) multiply an string by an integer, you split the string into characters, repeat each character a number of times equal to the integer, and then stick ...
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Iterate through addition of number sequence until a single digit [closed]
Challenge: With any given number that has multiple digits, every digit in the number needs to repeatedly be summed together until the sum is a single digit number. To make things interesting, if there'...
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Carry-less sum given a base b
Given a list of positive integers \$\mathcal I=I_1,I_2,I_3,...,I_n\$ and a base \$b>1\$ return their "carry-less sum", i.e. represent \$\mathcal I\$ in base \$b\$ and sum digit-by-digit ...
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Cartesian - polar conversion couple
We don't have a challenge for conversion between Cartesian and polar coordinates, so ...
The challenge
Write two programs (or functions) in the same language:
one that converts from polar to ...
- 104k
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9
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Cryptic Multiplications
Given two non-negative integers e.g. 27, 96 their multiplication expression would be 27 x 96 = 2592.
If now each digits is ...
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votes
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answers
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Decompose number N into the sum of three triangular numbers [closed]
It is known that any natural number can be decomposed into the sum of three triangular numbers (assuming 0 is triangular), according to Fermat's Polygonal Number Theorem. Your task is to come up with ...
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Implement Binary Exponentiation
Background
In programming, there is a recursive algorithm called binary exponentiation, which allows for large integer powers to be calculated in a faster way. Given a non-zero base \$x\$ and a non-...
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Extract the contained powers of two!
Take as input an integer in any reasonable format.
Then, output all the proper sub-strings of the base-10 digits of that integer that are powers of two, in any reasonable format.
Test cases
...
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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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7
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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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votes
27
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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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votes
12
answers
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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 {...
- 49.3k
18
votes
4
answers
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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 ...
- 49.3k
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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 ...
- 301
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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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votes
15
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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" ...
- 104k
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votes
10
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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, \...
- 104k
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votes
3
answers
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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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10
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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}\...
- 104k
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votes
14
answers
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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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vote
11
answers
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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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votes
14
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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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votes
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answer
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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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votes
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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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