Questions tagged [arithmetic]

Challenges related to elementary arithmetic.

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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 ...
Siddharth Singh's user avatar
11 votes
12 answers
2k views

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 ...
enzo's user avatar
  • 2,083
20 votes
14 answers
1k views

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 ...
ZaMoC's user avatar
  • 24.9k
23 votes
12 answers
4k views

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 ...
msh210's user avatar
  • 3,443
13 votes
21 answers
4k views

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 ...
corvus_192's user avatar
  • 5,087
24 votes
23 answers
4k views

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\$ ...
xnor's user avatar
  • 145k
9 votes
11 answers
741 views

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. ...
Luis Mendo's user avatar
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44 votes
18 answers
3k views

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 ...
blaketyro's user avatar
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22 votes
25 answers
4k views

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 ...
blaketyro's user avatar
  • 799
24 votes
5 answers
2k views

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 ...
Wheat Wizard's user avatar
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13 votes
72 answers
3k views

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 ...
Aitzaz Imtiaz's user avatar
11 votes
9 answers
1k views

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 ...
Michael M.'s user avatar
16 votes
15 answers
1k views

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 ...
l4m2's user avatar
  • 23.9k
5 votes
21 answers
515 views

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'...
Larsenv's user avatar
  • 87
19 votes
25 answers
2k views

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 ...
loopy walt's user avatar
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15 votes
20 answers
1k views

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 ...
Luis Mendo's user avatar
  • 104k
19 votes
9 answers
1k views

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 ...
Domenico's user avatar
  • 2,273
2 votes
0 answers
365 views

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 ...
Study's user avatar
  • 45
15 votes
16 answers
1k views

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-...
Aiden Chow's user avatar
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12 votes
17 answers
1k views

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 ...
Qaziquza's user avatar
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5 votes
19 answers
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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 ...
Number Basher's user avatar
17 votes
12 answers
2k views

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 <...
Jitse's user avatar
  • 7,016
9 votes
2 answers
330 views

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 ...
xiver77's user avatar
  • 2,365
15 votes
7 answers
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 ...
Peter Kagey's user avatar
  • 8,679
10 votes
5 answers
612 views

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\$ ...
Julian's user avatar
  • 3,028
26 votes
27 answers
2k views

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 ...
talex's user avatar
  • 711
28 votes
12 answers
2k views

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 {...
caird coinheringaahin g's user avatar
18 votes
4 answers
704 views

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 ...
caird coinheringaahin g's user avatar
15 votes
41 answers
1k views

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 ...
Rowan McAlpin's user avatar
6 votes
6 answers
396 views

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,...
DjinTonic's user avatar
  • 636
25 votes
11 answers
2k views

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 ...
DjinTonic's user avatar
  • 636
39 votes
15 answers
2k views

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" ...
Luis Mendo's user avatar
  • 104k
19 votes
10 answers
1k views

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, \...
Luis Mendo's user avatar
  • 104k
8 votes
3 answers
835 views

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....
AndrewTheCodegolfer's user avatar
7 votes
3 answers
181 views

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 ...
Trebor's user avatar
  • 725
5 votes
10 answers
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 ...
ToonAlfrink's user avatar
  • 1,284
28 votes
13 answers
3k views

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}\...
Luis Mendo's user avatar
  • 104k
21 votes
14 answers
2k views

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 ...
emanresu A's user avatar
  • 37.8k
20 votes
6 answers
1k views

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 ...
cheems's user avatar
  • 619
11 votes
21 answers
3k views

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 ...
Der_Reparator's user avatar
14 votes
16 answers
632 views

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 ...
Underslash's user avatar
  • 1,729
1 vote
11 answers
248 views

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 ...
Rydwolf Programs's user avatar
17 votes
16 answers
3k views

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 ...
Rydwolf Programs's user avatar
16 votes
19 answers
1k views

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 ...
math scat's user avatar
  • 9,228
13 votes
14 answers
2k views

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+\...
atzlt's user avatar
  • 487
13 votes
8 answers
712 views

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 ...
anotherOne's user avatar
  • 1,091
10 votes
0 answers
168 views

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 (...
Mahkoe's user avatar
  • 281
-2 votes
2 answers
213 views

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 ...
Elimination's user avatar
40 votes
38 answers
3k views

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 ...
Adám's user avatar
  • 30.2k
33 votes
52 answers
4k views

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&...
Giuseppe's user avatar
  • 28.5k

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