Question 159
There are $n$ lights in a line, $n \ge 3$, numbered with numbers 1 through $n$. At the beginning each odd light in the line is turned on and each even light is turned off. In each move we may simultaneously change the state of three consecutive lights (turn on or turn off).
a. Prove that the order of the moves we make is not important for the final state of the lights.
b. For which numbers $n$ can we in a finite number of moves reach a state when each odd light in the line is turned off and each even light is turned on?
a. Prove that the order of the moves we make is not important for the final state of the lights.
b. For which numbers $n$ can we in a finite number of moves reach a state when each odd light in the line is turned off and each even light is turned on?