Multiple light switches which control one light and modular arithmetic

The problem I would like to discuss is the following. Most people have seen a room where there are two independent light switches. For instance, in some bedrooms the light can be turned on and off at the entrance door and also at a switch next to the bed. In this case you can turn on the light when you enter the room at night and then later turn off the light when you are already in bed. You can then turn on the light again using the switch at the door. Of course you can also turn on the light again using the switch at the bed. In fact, the light can be turned on and off at any switch in any sequence – i.e. each switch works independently of the state of the other switch.

The question is, how does this work?

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.