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

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

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

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

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

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

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