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.
72
questions
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
votes
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
votes
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
12
votes
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
votes
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
votes
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
votes
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 ...
