MathDB

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?

Problem Statement