IL-GILLIS 2015 Problem 6

Let $n\geq1$ be a positive integer. $n$ lamps are placed in a line. At minute 0, some lamps are on (maybe all of them). Every minute the state of the lamps changes: A lamp is on at minute $t+1$ if and only if at minute $t$ , exactly one of its neighbors is on (the two lamps at the ends have one neighbor each, all other lamps have two neighbors).

For which values of $n$ can we guarantee that all lamps will be off after some time?