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

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
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heinrich snipped-for-privacy@yahoo.com writes in article
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 outputs , and connection patterns ,,}, 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 mitre.org The above may not (yet) represent the opinions of my employer.
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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.
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snipped-for-privacy@vex.net | their own grave." -- EARTH GIRLS ARE EASY
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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

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heinrich snipped-for-privacy@yahoo.com wrote:

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
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Jerry Avins wrote:

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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Doghouse wrote:

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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Zak wrote:

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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Doghouse wrote:

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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On Tue, 31 Oct 2006 09:20:33 -0500, Doghouse

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.
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BFoelsch wrote:
...

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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Jerry Avins wrote:

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.
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heinrich snipped-for-privacy@yahoo.com wrote: ) 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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made in the above text. For all I know I might be
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Willem wrote:

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...

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wrote:

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.
--
Wim Benthem






















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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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Wim Benthem wrote:

This fella seemed to have the answer - Back in 1998 - Dunno
From: Gary Wachs - view profile Date: Fri, Jun 26 1998 12:00 am
Hello fellow electrical weenies,
In my pre-Dilbert days about a decade ago, I was an electrician.
There was this one little electrical wiring puzzle involving three-way switches that almost stumped me back then. It tooks a few days to figure it out.
It's still one of my favorites! Why? Because, to understand its significance, you have to learn a little bit about electrical wiring, as well as electrical code regulations. You may find it to be tricky, but the solution does exist. Although I worked with dozens of EE's and electricians, none have solved it.
I've developed a home page about it at http://www.geocities.com/SouthBeach/3761/ElectriPuzzles.html
Give it a shot! Let me know what you think. Please don't post the solution if you get it. If you give up, I'll email you the answer.
By way of comparison, I would compare my 3-way switch problem to Tavern
Puzzles's "Sneaky Pete" puzzle; both were equally frustrating and satisfying when finally solved. (http://www.tavernpuzzle.com /)
Good luck,
Gar
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LAI wrote:

A friend wrote him; but he was referring to another puzzle. He does not know the answer either.
The reasoning leading to one SPDT and two DPDT switches cannot be correct, because the standard solution is already simpler: 2 SPDT and 1 DPDT switch.
Maybe the reasoning can be posted, so that we can check and maybe refine it?
Heinz
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LAI wrote:
...

I get "Sorry, the page you requested was not found." Is the URL correct?
...
Jerry
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rights of the vilest and most abhorrent are protected."
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