Roth’s Theorem (1953): any subset of the integers 1…N of sufficiently large density contains a 3‑term arithmetic progression (3‑AP). In this game you try to pick as many numbers as possible without creating a 3‑AP.
Two‑player mode is a friendly nod to van der Waerden’s theorem. A famous fact is W(2,3)=9, meaning any red/blue coloring of 1…9 forces a monochromatic 3‑AP—so someone must lose by then!
Tip: A 3‑AP is a triple (a, b, c) with equal gaps, like (4, 7, 10) or (3, 5, 7).