Questions tagged [arithmetic]
Challenges related to elementary arithmetic.
548 questions
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Compute the NFL passer rating
Each quarterback in the NFL is given a passer rating at the end of the game, which measures how good their forward passes were. It is not strictly a basic arithmetic formula, and is calculated as ...
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Fill in the blanks of this equation
Your task is to write a program or function that can fill in the blanks of an equation provided in this form:
_ + _ / _ = 4
In this case, a valid solution would be:
2 + 8 / 4 = 4
Each blank must be ...
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Find all unique quintuplets in an array that sum to a given target
Inspiration: Leetcode's [3Sum] link
Problem
Given an array nums of n (not necessarily distinct) integers, and given a target ...
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Complex Exponentiation [closed]
As the title says! Raise one complex number to the power of another.
(a+bi)^(c+di)(using the principal branch of the complex logarithm)
Requires four inputs a, b, c, d. You can combine a, b, c, d into ...
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Infer pluses and minuses
The problem
Consider an equation such as "3 ± 2 ± 4 ± 1 = 4" and determine if there exists a sequence of pluses and minuses that makes it arithmetically correct. If it exists, ...
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Number of cigarettes that can be made from a given number of butts
Assumption
A cigarette can be made by combining four cigarette butts. Cigarette butts last infinitely until smoked.
Explanation
Say you have 31 butts. That means, you can make 7 cigarettes from 28 ...
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12
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Solve a squared cryptarithm
Inspired by Greg Martin's "Shiny cryptarithm" puzzle.
A cryptarithm is a game consisting of a mathematical equation among unknown numbers, whose digits are represented by letters of the ...
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Number of ways to partition n into n = K + ꓘ
In this challenge you are asked to find in how many ways we can express a positive integer n as the sum of two positive integers ...
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80% of respondents agreed…
Sometimes I see a claim like "80% of respondents agreed" and I think "what was your sample size? 5?" because, of course, with a sample size of 5 it's possible to get 80% to agree ...
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German pharmacy payment
Your task is to calculate the amount you have to pay for prescribed medication at a pharmacy in Germany. The amount is simply based on the full price of the item, which will be your input. It is a ...
- 5,952
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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. ...
- 107k
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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 decimal digits.
Rules
Your program must take a non‐negative integer as input.
Your program should output the sum of the digits of the ...
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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 ...
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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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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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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
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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