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

heinrich_neumaier@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.

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.
--
Mark Brader, Toronto   |  "Men!  Give them enough rope and they'll dig
msb@vex.net            |   their own grave."    -- EARTH GIRLS ARE EASY

My text in this article is in the public domain.

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".  

heinrich_neumaier@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
--
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

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.

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

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
--
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

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
--
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

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.

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
--
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

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

On 31 Oct 2006 13:26:46 -0800, heinrich_neumaier@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.

heinrich_neumaier@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
--
Disclaimer: I am in no way responsible for any of the statements
            made in the above text. For all I know I might be
            drugged or something..
            No I'm not paranoid. You all think I'm paranoid, don't you !
#EOT

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...

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




















 

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)


--
Wim Benthem

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

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

LAI wrote:

   ...


I get "Sorry, the page you requested was not found." Is the URL correct?

   ...

Jerry
--
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯