xeroxia wrote: In the beginnig, each square of a strip formed by $n$ adjacent squares contains $0$ or $1$. At each step, if a square contains $0$ and exactly one of its neighbour contains $1$, we are writing $1$ instead of $0$ into that square, and we are writing $0$s into the other squares. Determine all possible values of $n$ such that whatever the initial arrangement of $0$ and $1$ is, after finite number of steps, all squares can turn into $0$. I think there is missing something. For example, what about the initial configuration when we assign 1 to all the squares?

MariusBocanu wrote: xeroxia wrote: In the beginnig, each square of a strip formed by $n$ adjacent squares contains $0$ or $1$. At each step, if a square contains $0$ and exactly one of its neighbour contains $1$, we are writing $1$ instead of $0$ into that square, and we are writing $0$s into the other squares. Determine all possible values of $n$ such that whatever the initial arrangement of $0$ and $1$ is, after finite number of steps, all squares can turn into $0$. I think there is missing something. For example, what about the initial configuration when we assign 1 to all the squares? I have changed the problem statement. In fact, Turkish version is also difficult to understand. I am not sure the corrected version, either.