MathDB

Let

n > 1

be a natural number. There are

n

bulbs in a line, each of which can be on or off. Every minute, simultaneously, all the lit bulbs turn off and the unlit bulbs that were adjacent to exactly one lit bulb turn on. Determine for what values of

n

there is an initial arrangement such that if this process is followed indefinitely, all the lights will never be off.

Problem Statement