A variant of the well known Infected Checkerboard problem. If we've a 𝑛x𝑛 square, then we fold it along top and bottom row to form a cylinder. A cell in this cylinder becomes infected if at least two of its neighbors (orthogonal only) are infected. Prove that, initially, if the number of infected cells is less than 𝑛, the whole cylinder can't be infected.
Additionally, instead of cylinder, let's form a torus by joining the sides of the square. Prove that 𝑛-1 initial infected cells are necessary to infect the whole torus.
The square variant can be solved by observing the perimeter of the infected cells.