# Switches needed in an n-location multiway switching system

Wikipedia shows us we can construct a two location multiway switching system with two 3-way switches:

They also teach us how to perform three location multiway switching with two 3-way switches and one 4-way switch:

Is it possible to make a similar system (three locations, all able to switch the light in any situation) with only three 3-way switches?

What can be said in general about the switches needed to make an n-location multiway switching system?

• This is a fun question, a good puzzle. The answer to the first part is, no, it can not be done. You might try asking on Mathematics SE, they might come up with some 'ring group algebra' (not just boolean) that could prove it can not be done. – Bobbi Bennett Mar 30 '13 at 15:31
• @BobbiBennett: Sure it can be done, even with as many as four distinct "3-way" switches, if one has a couple resistive elements (perhaps lightbulbs that are of higher wattage than the bulb one is trying to control, which are placed in a lightproof box). Wire the two "extra" bulbs using normal three-way circuits [two switches on each]. Then wire the bulb one actually wants to control between the hot sides of the two "extra" bulbs. Flipping any switch will change the state of that final bulb. Not a practical circuit, and horribly against code, but it would work. – supercat May 10 '13 at 15:01

What you call "three-way" switches I'd call "two-way" switches because they switch one of two ways - just a minor thing really. The middle switch in the 3-location scenario can be made from 2 x 2-way switches but they need to be "ganged" so they both operate together: -

To make n-location switching you repeat the middle dual-switch circuit from above - two wires in and two wires out. Repeat n times. It's an Exclusive or function.

4-location switch: -

Is it possible to just use 1 x SPDT switch per position - I think not but i'd like to see it disproven

• But, that is just a 4-way (DPDT)!? Or, it is two 3-way switches per n above 2. Camil Staps had specified only 3-way (SPDT) switches. This is kind of a cheat of an answer. – Bobbi Bennett Mar 30 '13 at 15:14
• @BobbiBennett ooh, now I see. Good point. This answers says something useful about n locations (that it is possible with the solution he provides), but doesn't answer the first question about the 3-location one without DPDT switches. – user17592 Mar 30 '13 at 15:30
• I would be happier if @Andyaka came right out at the top with 'it can not be done with only 3 SPDT switches'. Ecstatic if he could prove it! – Bobbi Bennett Mar 30 '13 at 15:33
• @BobbiBennett - it can't be done with only 3 x SPDT switches. I hope you are happier now LOL!!! – Andy aka Mar 30 '13 at 16:06
• @Andyaka, edit, so I can change my vote! – Bobbi Bennett Mar 30 '13 at 16:25