Questions tagged [rational-numbers]

This challenge involves the manipulation of rational numbers, i.e. those which can be represented as a fraction of integers. Do not use this tag if rational numbers are just one of several admissible input/output formats, but rather if the use of exact rational arithmetic is required.

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14
votes
14answers
465 views

Repetend length in 1/n

This problem is based on non-terminating, repeating decimal points. Let \$n\$ be any positive integer \$(n > 1 \text{ and } n < 10000)\$, say \$7\$. Then, \$1/n = 1/7 = 0.142857142857142857...\$ ...
12
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13answers
1k views

Diophantine Approximation: find lowest possible denominator to approximate within given precision

Challenge Given a number x and a precision e, find the lowest positive integer q such that <...
14
votes
5answers
547 views

Cantor Function, Cruel

A ripoff of this challenge. Go upvote it! Objective Given a rational number amongst \$[0,1]\$, apply the Cantor function to it and output the rational number that's produced. The Cantor function The ...
14
votes
12answers
2k views

Parse a Unicode vulgar fraction

Objective Given a string with single Unicode vulgar fraction, parse it to a rational number. Valid inputs A valid input is one of: ¼ U+00BC; one quarter ...
3
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5answers
109 views

Find the binary period [duplicate]

We know that not all fractions have a terminating binary representation. However every fraction can be written as a leading portion followed by a repeating portion. For example \$1/3\$ starts with \$...
38
votes
13answers
3k views

Phony fractions

Context If a0 and b0 are two decimal numbers, with a and ...
12
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9answers
1k views

Integer Logarithm

Objective Take \$a \in ℤ_{>1}\$ and \$b \in ℤ_+\$ as inputs. Write a function \$f\$ such that: $$ f(a,b) = \left\{ \begin{array}{ll} \log_ab & \quad \text{if} \space \log_ab \in ℚ \\...
27
votes
11answers
4k views

Rational Number RNG

The Objective Build a random number generator whose range is \$\left[0,1\right) \cap \mathbb{Q} .\$ This is, build a random number generator that can produce any value that's: at least \$0 \,;\$ ...
10
votes
7answers
1k views

Approximate the perfect fifth

Starting at 1-TET, give equal temperaments that have better and better approximation of the perfect fifth(just ratio 3/2). (OEIS sequence A060528) The formal description of the sequence, copied from ...
17
votes
63answers
4k views

Round towards zero

This is a simple task. Given a positive or negative real number, round it to the next whole integer closer to zero. The challenge Take input through any reasonable form (stdin, function, etc.) of ...
5
votes
1answer
386 views

Surreal Numbers

Surreal Numbers Surreal numbers are one way of describing numbers using sets. In this challenge you will determine the value of a surreal number. Intro A surreal number consists of two sets: a left ...
16
votes
7answers
691 views

Satisfying Rounding

Satisfying Rounding You know when you're in science class, and asked to round to 2 sig figs, but your answer is 5.2501...? You should round to ...
13
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6answers
1k views

Ryley's Theorem

S. Ryley proved following theorem in 1825: Every rational number can be expressed as a sum of three rational cubes. Challenge Given some rational number \$r \in \mathbb Q \$ find three rational ...
33
votes
42answers
5k views

Half, Half Half, and, Half

Consider the following number sequence: \$ 0, \frac{1}{2}, \frac{1}{4}, \frac{3}{4}, \frac{1}{8}, \frac{3}{8}, \frac{5}{8}, \frac{7}{8}, \frac{1}{16}, \frac{3}{16}, \frac{5}{16}, \frac{7}{16}, \...
16
votes
8answers
1k views

Convert a percentage to a “simple” ratio

You run a political website, and have determined that people have a better intuitive understanding when the chance of winning or losing an election is expressed as a ratio ("5 in 7") than when it is ...
15
votes
25answers
2k views

Mixed Fraction Equality

In elementary school, children learn about proper fractions, where the numerator is less than the denominator, and thus the value of the fraction is less than one. Later, they are taught about ...
15
votes
16answers
2k views

Exact Partial Sum of Harmonic Series

Challenge Given a positive integer N, output the sum of the first N reciprocals as an exact fraction, which is represented as a ...
14
votes
9answers
818 views

Number the positive rationals

The positive rational numbers can be shown to be numerable with the following process: Zero has the ordinal 0 Arrange the other numbers in a grid so that row a, column b contains a/b Plot a diagonal ...
21
votes
20answers
4k views

I want my book to be away from this table

Story So I have a book that I want to separate from my table with nothing but other books. I want to know how many books do I need to achieve this with \$n\$ book lengths. Here's a visualization ...
17
votes
6answers
765 views

Delete the first periodic digit

We all know that whenever a rational number is written in decimal, the result is either terminating or (eventually) periodic. For example, when 41/42 is written in decimal, the result is ...
20
votes
2answers
627 views

Bitwise XOR of rational numbers

Introduction Every rational number between 0 and 1 can be represented as an eventually periodic sequence of bits. For example, the binary representation of 11/40 is ...
19
votes
3answers
618 views

Writing rational numbers as ratio of factorials of primes

Note: this challenge has been posted on the sandbox. Introduction This challenge is inspired by 2009 Putnam B1, a problem in an undergraduate mathematics competition. The problem is as follows: ...
11
votes
15answers
637 views

Repeated reciprocal

What you need to do is create a function/program that takes a decimal as input, and outputs the result of repeatedly taking the reciprocal of the fractional part of the number, until the number ...
18
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12answers
1k views

LCM of Rational Numbers

The least common multiple (LCM) of a set of numbers A is the smallest integer b such that b/a...
15
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25answers
1k views

Adding fractions

Write a program or a function that takes two non-empty lists of the same length as input and does the following: uses elements of first list to get numerators, uses elements of the second list to get ...
34
votes
48answers
4k views

Infinitely Print Zeno's Dichotomy Paradox (1/(2^n))

Wikipedia: Zeno's Dichotomy Paradox An infinite number of mathematicians walk into a bar. The first one orders a beer. The second one orders half a beer. The third one orders a fourth of a beer. The ...
21
votes
2answers
431 views

Rational decomposition a = xyz(x+y+z)

Write functions x(a), y(a) and z(a) such that for any rational ...
7
votes
5answers
334 views

The Imperial Ruler

Given a ruler length in inches and fractions of an inch, and a granularity in fractions of an inch, output the values of all marks on the ruler, starting from 0, in ascending order. Input ruler length ...
9
votes
1answer
524 views

Fraction Frenzy!

EDIT: I'm getting a lot of comments about this not terminating - I will give the "correct answer" tag to either the first person who gives me FF(3) (as in provides ...
20
votes
9answers
2k views

Is it within the Cantor set?

The Challenge For this challenge, you are supposed to determine if a given number is in the Cantor set. So first, let's define the Cantor set. First, start with the numbers between 0 and 1. Any ...
20
votes
2answers
493 views

Swap out some periodic and non-periodic parts

In the decimal representation of every rational number p/q, you have a periodic tail, a non-periodic head, and a section before the decimal point in the following ...
16
votes
3answers
294 views

Golfed decimal fractions

Your goal is to write some code that will output the shortest unique decimal sequence for the input fraction. No two fractions with the same denominator may have the same output, although it's ...
27
votes
12answers
654 views

The nth numerator

You can create a list of all rationals 0 < r ≤ 1 by listing them ordered first by denominator and then by numerator: ...
22
votes
22answers
3k views

Simplify a continued fraction

Continued fractions are expressions that describe fractions iteratively. They can be represented graphically: Or they can be represented as a list of values: ...
29
votes
24answers
2k views

Output the nth rational number according to the Stern-Brocot sequence

The Stern-Brocot sequence is a Fibonnaci-like sequence which can be constructed as follows: Initialise the sequence with s(1) = s(2) = 1 Set counter ...
22
votes
6answers
1k views

Fraction to exact decimal

Write a program or function that given two integers a, b outputs a string containing a decimal number representing the fraction a/b exactly. If a/b is integer, simply output the value, without a ...
7
votes
9answers
574 views

Continued Fraction of a Rational Number

The continued fraction of a number n is a fraction of the following form: which converges to n. The sequence ...
6
votes
7answers
752 views

Calculate the Gamma function for half-integer arguments

Gamma function is defined as It is a well-known fact that for positive integers it coincides with a properly shifted factorial function: Γ(n) = (n - 1)!. However, ...
12
votes
13answers
2k views

In-between fractions

In-between fractions The challenge: You will need to create code that takes atleast 3 inputs; 2 integers and "a fraction representation" - whichever type suits your language for representing the ...
3
votes
3answers
712 views

Solve a quadratic equation using Vieta's formulas

Exposition Your mathematics teacher is a big fan of Vieta's formulas, and he believes that you should use them to solve quadratic equations. Given the equation ...
11
votes
6answers
506 views

Can a fraction be simplified using Anomalous Cancellation?

Anomalous Cancellation (from Wolfram Alpha): Anomalous cancellation is a "canceling" of digits of a and b in the numerator and denominator of a fraction a/b which results in a fraction equal to the ...
20
votes
33answers
1k views

Mixed Number to an Improper Fraction

Mixed Number to an Improper Fraction In this challenge you will be converting a mixed number to an improper fraction. Because improper fractions use fewer numbers, your code will need to be as short ...
15
votes
1answer
428 views

When Bullets Collide

This challenge is based off a riddle I read in some book a while ago, which I found again here. It is about bullets fired from a gun once per second at varying speeds that travel in a straight line ...
11
votes
4answers
522 views

Calculate the p-adic norm of a rational number

Calculate the p-adic norm of a rational number Write a function or a program, that takes 3 integers m,n,p (where p is a ...
23
votes
18answers
2k views

Lookalike shapes

Similar figures Two rectangles are similar if the ratios of their sides are the same. Consider these two rectangles; a rectangle 5 lines tall and 11 chars wide: ...
40
votes
6answers
2k views

World Big Dosa​

You are a talented young chef who has just been offered the position of sous chef at the world's most prestigious Indian restaurant. You have little experience with preparing Indian cuisine, but you'...
10
votes
4answers
1k views

Calculate a probability exactly

This task is about writing code to compute a probability exactly. The output should be a precise probability written as a fraction in its most reduced form. That is it should never output ...
13
votes
1answer
869 views

XKCD Bracket Probabilities

Today's XKCD is a sports-tournament style bracket, where the contestants are well-known names, put into groups of possibly confusing names. Give the probability that a given contestant will win the ...
9
votes
1answer
234 views

Determine whether rational coordinates are in the right Sierpinski triangle

The Sierpinski triangle is a set of points on the plane which is constructed by starting with a single triangle and repeatedly splitting all triangles into four congruent triangles and removing the ...
17
votes
7answers
1k views

Convert a fraction to a repeated decimal

Almost the polar opposite if this challenge, and I suspect it will be slightly easier. Your task is to take two integers in the format a/b (Forming a rational ...