Ninety-nine infected squares on a board of ten thousand. If you place them cleverly, can the infection take over every last square?
The Board Infection
Riddle statement
On a \(100\times100\) board, you may choose exactly 99 squares to be infected initially.
The infection then spreads in rounds: in each round, every healthy square sharing a side with at least two infected squares becomes infected. Infected squares never recover.
Can you choose the 99 starting squares so that, sooner or later, the entire board becomes infected?