Shown above is an animation of a circuit using three switches to control a light. The center switch is 4-way switch, while the outer two switches are 3-way.
For a discussion of how to wire such circuits, see 3-way and 4-way light switches. That page and its links also discuss proper wire colors and several wiring alternatives.
Note that in the above animation the wires are color coded to indicate their voltage state, not proper electrical code colors for their insulation. In particular, above we use the following convention:
For the lamp to turn on, we need a hot (red) wire to reach all the way from the voltage source on the left to the lamp on the right. For the lamp to burn, the switches must be configured to provide a complete circuit from the voltage source on the left to the lamp. Routing the voltage to a dead end means the lamp will be off.
You may view the above animation frame by frame at How 4-way switches work -- frame by frame.
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