# The other three switch puzzle: how to wire them all to a singe light

• posted

There is an old puzzle that asks how to wire three three-way
switches in such a way that each of them can switch on or
off a lamp. I read abou it at least 30 years ago.
This is NOT the puzzle about the three switches that you find
everywhere. In fact, the wiring is not trivial - it is not an easy
puzzle. I saw the solution once, but cannot find it
anywhere.
The puzzle is to find a 3 x "3-way switch" solution; the easy
2 x "3-way" plus 1 x "four-way" switch wiring
is not what I am looking for. (And no electrical regulations
should be followed; if I remember correctly, both ends of
the lamp are switched.)
Is anybody able to do this?
Heinz
• posted
heinrich snipped-for-privacy@yahoo.com writes in article dated 30 Oct 2006 13:51:16 -0800:
I'm not sure I understand exactly what you mean by "3-way switch".
If you assume it's a dial with inputs {1,2,3} outputs {A,B,C}, and connection patterns {{1A,2B,3C},{2A,3B,1C},{3A,1B,2C}}, you can do it for an arbitrary number of switches by hooking them up in series (3 wires between each adjacent pair of switches) and hooking the power-input and power-to-light wires up to arbitrary positions on opposite ends. So that's probably not what you mean.
--Keith Lewis klewis {at} mitre.org The above may not (yet) represent the opinions of my employer.
• posted
Heinrich Neumaier:
Keith Lewis:
This is a common usage where I live: it means a single-pole, double- throw switch. That's the kind used in pairs in household wiring when you want a light that can be turned on or off from each of two positions. In a triumph of idiom over logic, the same device is also commonly called a "two-way switch". (To be fair, it does have two positions and three terminals.)
A "four-way switch" in the same terminology is a double-pole, double-throw switch with two pairs of its six real terminals permanently connected, giving the effect that in one position it connects terminals A to B and C to D, and in the others, A to C and B to D. These can be used together with a pair of three-way switches to give additional positions where a single light can be turned on or off:
3-way 4-way 3-way ------ ------ ------< X >------ light power ------ ------ | supply | ------------------------------'
Heinrich's reference to a "4-way switch" shows that this is indeed the terminology he's using. He's asking for a way to achieve the same effect using three 3-way (single-pole double-throw) switches only.
• posted
I think it's like the puzzle whose answer cost me a technician job years ago. It labeled me "overqualified". A pair of three-way switches control a light in the tail of an airplane. The tail gunner and the pilot could both control the light. Wiring consists of two wires, using the airframe as return. The need arose for unswitched power in the tail, but there's no opportunity to run more wiring. What to do?
Jerry
• posted
Yes, the puzzle asks for three "single pole, double throw" switches. (Often called "three-way" switches.) The solution is not easy. Does anybody know it?
Heinz
"3-way switch".
• posted
Call the two wires A and B. Get a SPDT relay. Coil connected from A to frame. NO contact connected to A. NC contact connected to B. Load connected to Common.
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To get truly uninterrupted power, use one of the wires as power, the other to signal the switch position to the relay.
Use the relay and the switch in the rear to build the light bulb circuit.
Thomas
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No relay needed. Either switch (the pilot's or the gunner's) turns the light off if it is on of off if it is on. The gunner has power for his electric razor whether the light is on or off. The power source is near the pilot.
Jerry
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A wire brings power from the front of the plane to the tail. Both switches are SPDT, with one contact connected to power, the other connected to ground. (Code doesn't allow this because some switches might not be break-before-make.) The common terminal on each switch connects to one side of the light bulb.
Jerry
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It can be done without the relay.
At the pilot end connect the wiper to a wire to the tail. NO to hot, NC to frame. Run the hot to the tail. You now have two wires to the tail, hot and wiper.
At the tail, connect the second switch the same as the first, NO to hot, NC to frame. Connect the light between the two wipers.
• posted
...
Yes. I suspect that the solution to Neumaier's puzzle involves a connection of this kind. That's what brought it to mind.
Jerry
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In message , Jerry Avins writes
Don't you just hate those questions designed to find out if your too technical for the job. You see the question and you think it's unusually complex for the type of people who might apply.
I remember as part of the interview test for a job as an arcade technician there was a question that said "What is the formula for capacitive reactance.) OK, I know it's Xc=1/(2pieFC) but I just put a question mark in the box. I still came across as too technical for the job despite acknowledging that it was primarily board swapping.
• posted
Probably. But we are talking about 3 switches, not two. I searched google for a long time; but I found nothing about how to wire 3 switches to a lamp...
Heinz
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On 31 Oct 2006 13:26:46 -0800, heinrich snipped-for-privacy@yahoo.com proclaimed to the world:
I have seen it somewhere not too long ago. If I can remember where, or how to wire it, I will post it.
• posted
) Probably. But we are talking about 3 switches, not two. ) I searched google for a long time; but I found nothing ) about how to wire 3 switches to a lamp...
Is there no way to exhaustively number all possible ways to connect three switches and a lamp to power and ground ? You can apply some heuristics to quickly disallow certain connections, I think.
SaSW, Willem
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No need to exhaustively test.
The solution is
(A AND B AND C) OR (A AND NOT B AND NOT C) OR (NOT A AND B AND NOT C) OR (NOT A AND NOT B AND C)
Now if I just could figure out how to translate that to physical wiring...
• posted
There are many equivalent ways of writing this boolean expression, all of wich might have a translation with 3 switches.
physical wiring has possibilities you do not get with boolean logic: wires can have 3 kinds of signals on them: Power, ground and "not connected", and switches can let signals through in more than 1 direction.
I'm starting to suspect that there is no solution for this, using only 3 3-way switches, power, ground and a lamp. I've already written a program that can produce all possible ways to connect 3 switches, 6 wires, power, ground and a lamp. (a wire here is something that ties any number of terminals of components together)
Since any terminal can be connected to only one wire and all wires will connect at least 2 terminals, there can be a maximum of 6 wires.
The circuit is then represented as a set of 13 numbers wich represent the wires that the following terminal are connected to.
1 power 2 ground 3 switch 1 input 4 switch 1 output 1 5 switch 1 output 2 6-8 switch 2 9-11 switch 3 12 lamp 1 13 lamp 2
this means that there are at most 6^13 possibilities.
by eliminating permutations of the wires, the output terminals of the switches and the lamps, I've been able to reduce this to just 648769 possibilities. The hard part will be determining wether any of them is a solution.
• posted
Get a SPDT relay. Hook the common terminal to your output, and the two input wires to the "connected-when-coil-energized" and "connected-when-coil-not energized" terminals. Also run the wire from the "connected-when-coil-energized" terminal to the coil. Ground the other side of the coil.
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First, the relay isn't in the original bill of materials. Second, you haven't explained well enough for me to( understand how each of the switches can change the state of the lamp.
Jerry
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There seem to be no solutions, not even solutions that have the wrong outcome for the lamp in only one of the 8 switchcombinations. It seems that you can't do better than A and (B XOR C).
With 2 switches i've found that there are 3 different ways of wiring them:
one with the common terminals of the swithces connected to each other, one with the common terminals connected through the lamp, and one where both of the non-common terminals of the switches are connected to each other (this is the one actually used in practice)

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