Consider a 4 4 grid with light-up squares. In the starting configuration, some subset of the squares are lit up. At each stage, a square lights up if at least two of its immediate neighbors (horizontal or vertical) were "on" during the previous stage. It's easy to see that for the starting configuration in which four squares along a diagonal of the board are lit up, the entire board is eventually covered by "on" squares. Several other simple starting configurations with four "on" squares also result in the entire board being covered. Is it possible for a starting configuration with fewer than four squares to cover the entire board? If yes, find it; if no, give a proof