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Questions tagged [open-ended-function]

For challenges where an exact output is not required but some property must still be fulfilled.

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82 votes
84 answers
8k views

Print some JSON

This challenge is straightforward, but hopefully, there are plenty of avenues you can approach it: You need to print/return a valid JSON object of at least 15 characters, not counting unessential ...
Nathan Merrill's user avatar
67 votes
165 answers
11k views

Print all integers

Write a program or function which will provably print all integers exactly once given infinite time and memory. Possible outputs could be: ...
Fatalize's user avatar
  • 38.8k
57 votes
37 answers
5k views

Turing-Complete Language Interpreter

A challenge I thought that would be very cool is to make an interpreter for a Turing-complete language of your choosing. The rules are simple: You may use any language to create this interpreter ...
arodebaugh's user avatar
51 votes
30 answers
12k views

What an Odd Function

Your task here will be to implement a function1 that forms a permutation on the positive integers (A bijection from the positive integers onto themselves). This means that each positive integer ...
Wheat Wizard's user avatar
  • 98.8k
47 votes
4 answers
4k views

f(g(x)) decreases while g(f(x)) increases

For this challenge you need to implement two functions, f and g, on the integers, such that f ∘ g is a strictly decreasing function while g ∘ f is a strictly increasing function. In other words, if ...
Martin Ender's user avatar
44 votes
32 answers
4k views

Define a function f such that f(f(n)) = -n for all non-zero integers n

This challenge was inspired by a programming blog I frequent. Please see the original post here: A Programming Puzzle Challenge Define a function \$f:\mathbb{Q}\to\mathbb{Q}\$ such that \$f(f(n)) = -...
ardnew's user avatar
  • 2,329
42 votes
70 answers
5k views

Infinitely many ℕ

Background: A sequence of infinite naturals is a sequence that contains every natural number infinitely many times. To clarify, every number must be printed multiple times! The Challenge: Output a ...
Adam Katav's user avatar
42 votes
21 answers
2k views

Three other numbers

Given three distinct numbers from \$1\$ to \$7\$, output three other distinct numbers from \$1\$ to \$7\$, that is having no numbers in common with the original numbers. Your code must produce a ...
xnor's user avatar
  • 145k
38 votes
58 answers
3k views

Output a random unary string

Your task is simple: output the letter x a random number of times. Every possible length of xs must have a non-zero probability ...
pxeger's user avatar
  • 23.9k
37 votes
20 answers
3k views

Egyptian fraction representations of 1

An Egyptian fraction is a representation of a rational number using the sum of distinct unit fractions (a unit fraction is of the form \$ \frac 1 x \$ where \$ x \$ is a positive integer). For all[1] ...
pxeger's user avatar
  • 23.9k
36 votes
1 answer
2k views

Write a program whose nontermination is independent of Peano arithmetic

Challenge Write a program P, taking no input, such that the proposition “the execution of P eventually terminates” is independent of Peano arithmetic. Formal rules (In case you are a mathematical ...
Anders Kaseorg's user avatar
35 votes
14 answers
3k views

Put together a Senate majority

There are one hundred members of the United States Senate. Assuming that nobody filibusters and that the Vice President isn't cooperating, at least fifty-one members are necessary to pass a bill. But ...
Sneftel's user avatar
  • 635
33 votes
10 answers
2k views

B​u​i​l​d a n​e​s​t

The challenge is simple: write a program or function that, when given a finite non-negative integer, outputs a nested array. The rules Your code must produce a unique valid nested array for every ...
ETHproductions's user avatar
32 votes
6 answers
1k views

Implement true string addition

Many languages allow strings to be "added" with +. However this is really concatenation, a true addition would follow the group axioms: It is closed (...
Wheat Wizard's user avatar
  • 98.8k
29 votes
20 answers
3k views

Transform characters of your choice into "Hello, world!"

Write a program or function that takes a character as input and outputs a character. Also, choose a list of 13 distinct ASCII printable characters (32-126). When a character from this list is passed ...
Jiří's user avatar
  • 1,885
28 votes
64 answers
3k views

Create an array with repeated numbers

Challenge Your task in this question is to write a program or a named function which takes a positive integer n (greater than 0) as input via STDIN, ARGV or ...
Optimizer's user avatar
  • 26.5k
28 votes
11 answers
2k views

Infinite ordinals from a well-ordering

Your task is to write a short program that represents a large (infinite) ordinal, using a well-ordering of the set of positive integers. Your program will take two different positive integers and ...
AnttiP's user avatar
  • 7,898
27 votes
17 answers
3k views

Give me odd, even, square, cube, prime and composite 3-digit numbers

Given a string which is guaranteed to be either odd, even, square, ...
Arnauld's user avatar
  • 193k
27 votes
9 answers
2k views

Walk Across a Keyboard

Given a word (or any sequence of letters) as input, you must interpolate between each letter such that each adjacent pair of letters in the result is also adjacent on a QWERTY keyboard, as if you ...
Vaelus's user avatar
  • 609
27 votes
6 answers
6k views

Golf a number bigger than Loader's number

As a follow up to Shortest terminating program whose output size exceeds Graham's number and Golf a number bigger than TREE(3), I present a new challenge. Loader's number is a very large number, ...
Christopher King's user avatar
26 votes
7 answers
1k views

Decode the Void

A void list is a list that at no level contains any non-list objects. Or if you prefer a recursive definition The empty list is void A list containing only other void lists is void All void lists ...
Wheat Wizard's user avatar
  • 98.8k
25 votes
10 answers
2k views

Floor of complex number

Background Complex floor is a domain extension of the mathematical floor function for complex numbers. This is used in some APL languages to implement floor , ...
Bubbler's user avatar
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25 votes
20 answers
1k views

Kolmogorov-simple numbers

If you visit Code Golf often, you may have heard of Kolmogorov complexity. It's usually defined as the amount of bytes required to express some string in a programming language. Here the Kolmogorov-...
AnttiP's user avatar
  • 7,898
24 votes
11 answers
3k views

Bijective function ℤ → ℤⁿ

It is trivially possible to create a bijective function from \$\mathbb{Z}\$ (the set of all integers) to \$\mathbb{Z}\$ (e.g. the identity function). It is also possible to create a bijective ...
Esolanging Fruit's user avatar
24 votes
16 answers
1k views

Every Possible Cycle Length

A function (or program) which takes inputs and provides outputs can be said to have a cycle if calling the function on its own output repeatedly eventually reaches the original number. For instance, ...
isaacg's user avatar
  • 42k
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
  • 98.8k
22 votes
24 answers
2k views

Generate an arbitrary half of a string

Given a string \$ x \$, we say another string \$ y \$ is half of it, if both of the following properties are true: \$ y \$ is a (not necessarily continuous) subsequence of \$ x \$ - there exists a ...
Command Master's user avatar
22 votes
17 answers
3k views

Don't repeat yourself

In this challenge you will be tasked with implementing a sequence of natural numbers such that: Each number appears a natural number of times No two numbers appear the same number of times No two ...
Wheat Wizard's user avatar
  • 98.8k
21 votes
13 answers
2k views

Output every sublist ... eventually

You will be given as input an infinite stream of positive integers. Your task is to write a program which outputs an infinite sequence of lists with two requirements: All lists in the output are ...
Wheat Wizard's user avatar
  • 98.8k
21 votes
15 answers
2k views

Output a 1-2-3 sequence

For the purposes of this challenge, a 1-2-3 sequence is an infinite sequence of increasing positive integers such that for any positive integer \$n\$, exactly one of \$n, 2n,\$ and \$3n\$ appears in ...
Tbw's user avatar
  • 2,083
21 votes
11 answers
2k views

Create a nibble shorthand

I recently stumbled across this image on wikimedia commons. It's a little bit of an information overload at first, but after examining it a bit it shows an interesting number system for writing ...
Wheat Wizard's user avatar
  • 98.8k
21 votes
10 answers
3k views

An unknowably odd function

This challenge initially appeared in this challenge as a an extra brain teaser. I am posting it with permission from the original author so that we can have a formal competition. Your task here ...
Wheat Wizard's user avatar
  • 98.8k
21 votes
2 answers
516 views

Rational decomposition

Write functions \$x(a)\$, \$y(a)\$ and \$z(a)\$ such that for any rational \$a\$ all functions return rational numbers and $$x(a) \times y(a) \times z(a) \times (x(a) + y(a) + z(a)) = a$$ You may ...
orlp's user avatar
  • 39.1k
20 votes
25 answers
3k views

Give f and g that sometimes commute

Let \$Z\$ be either the integers, the positive integers, or the non-zero integers; pick whatever's convenient. Give two functions \$f\$ and \$g\$, each \$Z \to Z\$, such that: \$f(g(a)) = g(f(a))\$, ...
cjquines's user avatar
  • 1,231
20 votes
9 answers
1k views

Split some points

proposed by @Adám in chat Given an even number of finite points return a line \$y=mx+b\$ that evenly splits the points on both sides. Specs Take a list of distinct points \$(x,y)\$ (or a list of x-...
math scat's user avatar
  • 9,408
19 votes
22 answers
3k views

Be big more often

Related You are a manager at a large number factory. You want to show everyone your business is doing well, by showing randomly chosen samples. Unfortunately, your business is not doing that well. But ...
The Empty String Photographer's user avatar
19 votes
9 answers
985 views

Output an infinitely proportional sequence

In this challenge, an infinitely proportional sequence is defined as a infinite sequence of positive integers such that: All positive integers are contained infinitely many times within the sequence. ...
emanresu A's user avatar
  • 38.8k
19 votes
10 answers
2k views

Enumerate the rationals

The cardinality of the set \$\mathbb Q\$ of rational numbers is known to be exactly the same as that of the set \$\mathbb Z\$ of integers. This means that it is possible to construct a bijection ...
att's user avatar
  • 20.6k
19 votes
1 answer
615 views

Demonstrate some advanced abstract algebra

Consider a binary operator \$*\$ that operates on a set \$S\$. For simplicity's sake, we'll assume that \$*\$ is closed, meaning that its inputs and outputs are always members of \$S\$. This means ...
caird coinheringaahin g's user avatar
18 votes
20 answers
1k views

Generate a regular graph

Inspired by this Mathematica.SE post Given two positive integers \$n, k\$ with \$n > k \ge 1\$, output a binary \$n\times n\$ matrix such that every row and column contains exactly \$k\$ 1s, and ...
caird coinheringaahin g's user avatar
18 votes
15 answers
2k views

Design a commutative injective function between any (restricted) infinite set and unordered pairs thereof

Related, but this only requires positive integers and does not have to be commutative The Cantor Pairing Function is described in this Wikipedia article. Essentially, it is an operation such that ...
hyper-neutrino's user avatar
  • 42.4k
18 votes
8 answers
873 views

Make every fixed list

We are to define the idea of a fixed list as follows: A fixed list is a list of fixed lists. This definition is recursive so it's useful to look at some examples. The empty list ...
Wheat Wizard's user avatar
  • 98.8k
18 votes
9 answers
1k views

Surjection from one string to two strings

This is the inverse of negative seven's question. Write a program or function which, given any single, possibly-empty string of printable ASCII (codes \$[32,126]\$) outputs or returns two strings of ...
GammaFunction's user avatar
18 votes
7 answers
2k views

Hilbert's binary Hotel

In this challenge you will be asked to implement any function (or full program) that fulfills two properties. Those properties are: Your function must be an injective (reversible) function from the ...
Wheat Wizard's user avatar
  • 98.8k
17 votes
15 answers
1k views

Enumerate all pure sets

In set theory, a set is an unordered group of unique elements. A pure set is either the empty set \$\{\}\$ or a set containing only pure sets, like \$\{\{\},\{\{\}\}\}\$. Your challenge is to write a ...
emanresu A's user avatar
  • 38.8k
17 votes
12 answers
1k views

Encode the input to exclude a given character (part 1)

Your task is to write 2 functions/programs. They may share code. The first function must, given a string and a character, output a new string that does not contain that character. The second function ...
mousetail's user avatar
  • 12.7k
17 votes
11 answers
2k views

Shortest total non-primitive recursive function

Natural numbers ≡ \$\mathbb{N}≡\{0,1,2,...\}\$ The submission can be either a program or a function, both cases will henceforth be referred to as "function". The task is to golf the shortest ...
user41805's user avatar
  • 13.1k
17 votes
14 answers
3k views

BigNum Bakeoff Reboot

Some of you may be familiar with the BigNum Bakeoff, which ended up quite interestingly. The goal can more or less be summarized as writing a C program who's output would be the largest, under some ...
Simply Beautiful Art's user avatar
17 votes
7 answers
1k views

As close to flat as possible

Write a program or function that fulfills the following Scores less than 101 bytes under normal code-golf rules Takes no input1 and always outputs a single integer. Every integer is a possible output....
Wheat Wizard's user avatar
  • 98.8k
17 votes
7 answers
2k views

Define the finite field GF(9)

\$GF(9)\$ or \$GF(3^2)\$ is the smallest finite field whose order isn't a prime or a power of two. Finite fields of prime order aren't particurlarly interesting and there are already challenges for \$...
nwellnhof's user avatar
  • 10.5k