binary

Numberphile with Daniel Erman on the Josephus problem, where people in a circle are eliminated in turn. It shows how the survivor's position follows a neat pattern tied to powers of two and binary.

Tom Scott explains for Computerphile how floating point numbers work, why moving the binary point is fast, and why it handles money badly.

Matt Parker of Stand-up Maths explains single-pile Nim and the trick that wins it, using Dr NIM, a 1960s mechanical plastic computer that plays perfectly. He teaches the strategy so viewers can beat friends.