puzzle solving

3Blue1Brown walks through a very hard Putnam competition problem and its elegant solution, emphasizing the visual intuition and the thought process behind solving it.

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.

Numberphile talks with Grant Sanderson of 3Blue1Brown about a darts puzzle with a shrinking bullseye. Solving it takes the volumes of high-dimensional spheres, and the answer turns up Euler's number.

A Veritasium video that runs the 2-4-8 rule-guessing puzzle on people to show how they test only examples that confirm their hypothesis. It uses this to illustrate confirmation bias and falsification.

3Blue1Brown visualizes high-dimensional spheres to explain a surprising puzzle about how a sphere fits in a box as dimensions grow. It builds geometric intuition for counterintuitive properties of high-dimensional space.

3Blue1Brown's chapter on eigenvectors and eigenvalues in the Essence of Linear Algebra series. It builds a visual intuition for what they mean, why an eigenbasis is useful, and ends with a puzzle.

Isaac Arthur examines the Dyson Dilemma, the puzzle of why we see no Dyson spheres or megastructures if growth-oriented civilizations should build them. He covers detectability and whether such structures could hide.