Subbasis. Generate. Discrete? Objective Given finitely many finite sets, interpret them as a subbasis to generate a space, and decide whether the resulting topology is discrete. Introduction to Topology Given a set \$X\$, a topology \$\mathcal{T}\$ over \$X\$ is a subset of the power set \$\mathc...

!!!Batch is another derivative of the Windows Batch programming language, its wiki is here Your challenge is to create an interpreter that reads a !!!Batch program and returns a Windows Batch program. In !!!Batch each character is converted to another ASCII character, like '?!?' -> 'a' and so on ...

Earlier, we did the pseudofactorial of a number, which is the LCM of the numbers from 1 to n. It would be useful in adding fractions together. However, we find that the denominator of 1/1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 is 20 instead of the pseudofactorial of 6, which is 60. Your task is to find...

Given a string with a multiple people's investment data, find out how much profit/loss they recorded. The string only contains capital and lowercase letters, like this: AABaBbba Each letter represents a person - a capital letter means buy, a lowercase letter means sell. The price of the stoc...

Given two inputs, a number n and a dimension d, generate the nth d-dimensional pyramid number. That was confusing, let me try again. For d = 1, the numbers start 1,2,3,4,5 and is the number of points in a line n points long. For d = 2, the numbers start 1,3,6,10,15 and is the number of points in ...

Background Character classes are a standard way to indicate a set of characters to match in regular expressions. For example, the class [ab] matches a or b, [a-z] matches any lower case letter, and [^a] matches everything but a. For the purpose of this question, classes can contain: a sequence o...

This challenge is to write a quine (program that can output itself) without reading any files. You can have the program be a print or output function containing a string of the program, but the program it outputs must also work under the same criteria. It cannot connect to a website with the code...

Snail word You know snails, they are sodium slow. And they have great looking shells. So let's decorate them Given a string as input, make a spiral shape from it. Let's define spiral for this challenge: Starting from a point A go one step in a chosen direction (left,right,up,down). And move arou...

This is a challenge to make a program that has an algorithm to modify itself to have a better algorithm or be more efficient. The algorithm must not have any randomness. The score is (bytes of original code * bytes of output code).

While at work I spotted a nice and simple challenge. The job was to stock products in cargo units with a certain capability. Since an order can have various batches, coming in sequence from the production, we usually make a list of the pieces of those batches distributed in each cargo to make sur...

Worldview of a programming language Is the glass half empty or half full? It's a common rethoric question to determine a person worldview, which can be optimistic or pessimistic based on the answer given. Let's try and see if programming languages have a worldview too. Write a full program or a f...

This challenge is to make a program copy itself to a new file, execute itself and the new file so each program doubles itself, and when there are 2048 copies of itself in existence, all of the files delete themselves, but they only delete themselves, not one program deleting every program. Also, ...

A binary relation on a set \$X\$ is simply a subset \$S \subseteq X \times X\$. The number of different relations grows quickly with the size of the set: if \$|X| = n\$, there are \$2^{n^2}\$ binary relations on \$X\$. This challenge will have you computing the number of binary relations subject ...