# 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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### Bijection between $\mathbb N$ and at-most-$n$-ary trees

Background Related: a golflang theory I posted in TNB a while ago At-most-$n$-ary trees are rooted trees where each internal node has between 1 and $n$ children (inclusive). Two trees are ...
109 views

### NP-complete reduction: (grid-)Hamiltonian circuit

Background Hamiltonian circuit problem is a decision problem which asks whether a given graph has a Hamiltonian circuit, i.e. a cycle that visits every vertex exactly once. This problem is one of the ...
2k 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, ...
283 views

### Venn of $n$ statements

Given a positive integer $n$, output $n$ 2D bool images with the same width and height such that: Each image should be 4-connected, i.e. for each two pixels that are true, you can start from one ...
671 views

### Encode a Lenguage

The Len(language,encoding) family of languages is a variety of Lenguage derivatives. To encode a program into a Len language, you replace every character with its representation in a certain encoding, ...
506 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 ...
404 views

### Rewrite strings without changing their order

Lexicographic Ordering For this challenge we will be talking about the lexicographic ordering of strings. If you know how to put words in alphabetical order you already understand the basic idea of ...
2k views

### Generate a mantis's head (symmetrical triangle)

Given guaranteed strictly positive integers $w$ and $n$, output An equilateral triangle array with side length $w$, filled with two distinct, consistent values. I'll call these ...
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 , ...
555 views

### Compute the uncomputable ... sort of

Implement a function $f$ (as a function or complete program), such that $\displaystyle\lim_{n\rightarrow \infty} f(n)$ converges to a number which is not a computable number. Answers will be ...
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 ...
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### Golf a bijection $\mathbb{N}^n\to\mathbb{N}$

Your task is to write a program which implements a bijection $\mathbb{N}^n\to\mathbb{N}$ for $n \ge 1$. Your program should take $n$ natural numbers as input, in any acceptable method (including ...
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 ...
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 ...
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 ...
988 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 ...
2k views

### Injection from two strings to one string

Challenge Write a program that applies an injective function which takes an ordered pair of strings as input and one string as output. In other words, each input must map to a unique output. ...
3k 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, ...
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 ...
1k 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 ...
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 ...
406 views

### Any digital permutation

Task Your task is to output a single integer, with one restriction: its digits must be a permutation of [1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6]. For example, you could output 653443653152432, ...
1k 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 ...
216 views

### Fabricate Frequently Factored Functions

In one of this question's bonuses I asked you to design a permutation on the natural numbers such that the probability of a random term being odd was $1$. Now let's kick it up a notch. I want you ...
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### 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 ...
208 views

### Two interwoven chains

In this question I defined a "chain" function as a function that: is a permutation, meaning that every value maps to and is mapped to by exactly one value. and allows any value can be obtained from ...
890 views

### Make an infinite chain

Lets define a class of functions. These functions will map from the positive integers to the positive integers and must satisfy the following requirements: The function must be Bijective, meaning ...
405 views

### Construct a Permuter

For this challenge you are going to make a function (your function may be a complete program) that takes a list as input and returns a permutation of that list. Your function must obey the following ...
963 views

### Golf a bijection within the natural numbers which map the primes to a proper subset of the primes

Definitions A bijection from a set S to a set T is a function from S to ...
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### 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 ...
466 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 ...
3k 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 ...
3k 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 ...
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### 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 ...
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### Map a list of indefinite size to a number!

It is well known, in the field of Mathematics studying infinity, that the Cartesian product of any finite amount of countable sets is also countable. Your task is to write two programs to implement ...
446 views

### One-to-one correspondence between pairs of integers and the positive integers

It is well-known that there are one-to-one correspondences between pairs of integers and the positive integers. Your task is to write code defining such a correspondence (by defining a pair of ...
541 views

### Pack sequences of non-negative integers

Let N be the set of nonnegative integers, i.e. {0, 1, 2, 3, ...}. Let c0(N) be the set of all infinite sequences in N that converge to 0, i.e. { (xn) ∈ NN | xn → 0 as n → ∞}. c0(N)...
526 views

### Add an integer to a set and take it back out

Definition: a set is a datatype which allows testing of inclusion ("does set X contain element Y?") but does not have order. Its size is the number of distinct elements it contains. Define an ...
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)) = -...