# Category: Maths

• ## Combinatorics of parentheses and binary operators

Combining parentheses and binary operators to calculate arithmetic properties, and reasoning about their recurrence relations and generic closed forms.

• ## Generating random data, part 2

Given various sources of random data on a Unix system, which are the most efficient while also producing sufficiently random data?

• ## Generating random data, part 1

Why are computers so bad at behaving unpredictably, and how can we generate random data effectively?

• ## Fixed points of hash functions

Under what circumstances can (or must) a fixed point of a cryptographic hash function exist: where a string hashes to itself?

• ## Mathematical quines

A demonstration of a mathematical quine: a formula which prints itself when graphed.

• ## The Monty Hall Problem

The somwhat counter-intuitive Monty Hall Problem, and a quick mathematical explanation and generalisation.

• ## Hangman strategy

The best strategy to use when choosing words in Hangman, depending on the number of guesses allowed and the length of the word.