Problem #WSP-5609

Problem

In the Game of Life, each cell in a grid is either alive or dead (in the diagram, yellow cells are alive). At each step, a live cell stays alive only if it has \(2\) or \(3\) live neighbours, otherwise it dies; a dead cell becomes alive only if it has exactly \(3\) live neighbours. A still-life is a pattern that does not change after any number of steps. Show that the following pattern cannot be turned into a still-life by only changing dead cells into alive cells.