# Solution: Multiple light switches which control one light

In a previous post (see here) I stated the problem of how to design an electric circuit with multiple light switches where the light can be turned on and off independently at each switch. Here I present the solution.

Solution for two light switches

For two switches, the following picture illustrates the solution. The switches can be in one of the four states as below. Each switch can be used to turn the light on or off, regardless of the state of the other switch.

For instance, if the switches are in state 1 (light turned on), then one can turn off the light using switch 1, in which case the switches are then in state 4. Alternatively, in state 1, the light can also be turned off using switch 2, in which case the switches are then in state 2.

Still, the question remains how one can design the circuit with $n=3,4,\ldots$ switches.

Solution for $n$ light switches

Let us now describe a solution if we have $n$ light switches. (Of course, a solution to this problem is known, so it is not the aim here to discover something new.) In this case we put a switch of the form below between Switch 1 and Switch 2 above.

The solution for ${}n$ switches is analogous to the solution for ${}3$ switches.