Ponder This Challenge - August 2026 - The Wheel of Buttons

Solving the game by hand for n=4n=4 is a good way to obtain a feel to the way a general solution works. Encode each state of the table as an element of F24\mathbb{F}_2^4, i.e. a sequence of 0 and 1 of length 4 (let 1 denote an off switch so that the goal is to reach 00000000).