A Simple Proof From the Pattern-Matching Card Game Set Stuns Mathematicians

In a series of papers posted online in recent weeks, mathematicians have solved a problem about the pattern-matching card game Set that predates the game itself. The solution, whose simplicity has stunned mathematicians, is already leading to advances in other combinatorics problems. Invented in 1974, Set has a simple goal: to find special triples called "sets" within a deck of 81 cards. Each card displays a different design with four attributes--color (which can be red, purple or green), shape (oval, diamond or squiggle), shading (solid, striped or outlined) and number (one, two or three copies of the shape). In typical play, 12 cards are placed face-up and the players search for a set: three cards whose designs, for each attribute, are either all the same or all different.