Demonstration

A stable matching always exists and is findable in O(n^2), but it's optimal for the proposing side. Mechanism design in twenty lines.

A compiler can hide a backdoor in itself with no trace in any source. The limit of source-code review, and what reproducible builds do about it.

Convince someone you know a secret while revealing nothing. The most counterintuitive constructive result in the series.

O(log n) proof that one item belongs to a huge set. Git, certificate transparency, and every blockchain are the same data structure.

Peterson's algorithm and Lamport's bakery. Correct mutual exclusion from plain reads and writes, and why modern hardware still breaks it (see Memory models and...

Constant space, no false negatives, a tunable false-positive rate, and the exact formula for the tradeoff.

Adding a node should move 1/n of the keys, not all of them. One idea, and virtual nodes to fix its variance (Balls into bins and the power of two choices).

How real systems dodge FLP impossibility: safety always, liveness only when the network cooperates.

What a hash function actually guarantees, as opposed to what it seems to do.