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

The Karnaugh map for this is

C C c c B b B b A 1 0 0 1 a 0 1 1 0

where a = not A, b = not B, c = not C

As you can see, any change in input A, B, or C inverts the output. There's also no simplification that I can see from the map.

Put in equation form gives

A ( BC + bc ) + a ( bC + Bc )

It's too hard to draw the resulting switching diagram using ascii, but I did it on paper, and the result I got was you need the following as a minimum:

switch A = single pole double throw switch B = double pole double throw switch C = double pole double throw

I don't see how it can be done with less.

dave y.

Which is the same as

(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)

Which is not three 3-way switches.

Yet, there is another claim of solution also with a hint of non-standard wiring.

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

There isn't, but in the UK, we use an "intermediate" switch which can do this. You can control a light from a pair of 3-way switches and any number of intermediate switches. (Note that outside the US, a changeover switch is called a 2-way switch, not a 3-way switch, as it has 2-ways.) See the following for diagrams: ttp://

In other European countries, this is more commonly done by using any number of momentary push buttons and an impulse relay (changes state every time the coil is operated), which is uually fitted in the panel.

Your "intermediate" switches are what we commonly call 4-way switches, which are internally cross wired DPDTs. They are also called "reversing switches" from their use in motor wiring.

When I first saw this puzzle, I thought the basis of the "tail-gunner's heater" problem might carry over, but I haven't gotten anywhere with it.

Jerry

More than a claim. The solution was posted earlier in this thread. (I didn't find it withe a quick look, so I can't credit the author. Here it is again: A B o-------o o------o / \ / power-----o / o------load-----ground C / \ D / o-------o o------o

There are other configurations, but this one meets code. The center switch is a "four-way", for its four terminals. It can be made by connecting the NO of each pole of a DPDT with to the NC of the other. Depending on its position, wires A - B and C - D are connected, or A - D and C - B. As many additional four-ways can be cascaded as needed.

The end switches are three-way -- SPST -- and pretty self explanatory.

Jerry

...

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

...

Jerry

Willem writes in article dated Tue, 31 Oct 2006 22:11:58 +0000 (UTC):

Sure, that's easy.

The 4 devices have a total of 11 connections, meaning there's a maximum of

Without loss of generality, you can assign "ground" to node 1 and "power" to node 2. At this point there are 11^11 possible hookups.

Then you can prune away:

• any hookup which has a disconnected partition

• any hookup which skips a node number (which means you'll never use a node beyond 9)

I'm going to go on record saying I think the solution must involve either a DPDT "4-way" switch or some kind of switching device (e.g. diode or relay).

--Keith Lewis klewis {at} mitre.org The above may not (yet) represent the opinions of my employer.

I think I finally see why in America a SPDT switch is called a three-way. A double-throw knife switch would have had three possible states. Is that a reasonable explanation?

Doghouse...

No, I think that it's much simpler than that. In the UK an SPDT is called a two-way switch because one input is switched between two ways. In the US it's called three-way because it has a total of three terminals - or "ways". Likewise a DPDT switch internally wired as a cross-over (or "intermediate") switch has four terminals and hence in US parlance it's a four-way switch. The problem is that "way" does not mean the same thing on both sides of the Atlantic.

David

The "claim" I was referring to was that of a solution using three 3-way switches, which is not what you show below.

And although a three 3-way solution has been claimed, no such solution has yet been posted.

=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF= =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF

I think it might just be that it has three terminals, unlike a "normal" switch with only two.

Well, I've been dealing with toggle switches for years, and the only classifications I ever heard of were 1/2/3 Pole single/double throw, with double throw possibly modified by center-off. Some throws could be momentary. Make before break is unusual, but make after break is usual (and generally safer).

SPST, SPDT, DPST, DPDT, 3PST, 3PDT ...

all can have momentary action. DT can have optional center off. Another rarity is triple throw, ie. DP3T. P counts common connections, T output connections per pole.

Rotaries are another story.

The relay wiring was in parallel to the existing wires, so the lamp state switching didn't change at all. But others have posted better solutions sans relay anyway.

I l don't see a solution for three SPDT switches controlling a lamp, though two SPDT plus one DPDT can do it easily.

On Thu, 02 Nov 2006 15:01:19 -0500, CBFalconer proclaimed to the world:

The terms "three way" and "four way" are used in the home electrical wiring industry only. My father learned electricity through apprenticeship and in turn I started out as a kid learning the common terms that electricians used. Back when he started most all electrical work was what we now call residential and industrial electricity was just beginning to use a different set of terms. For 99 out of a 100 "electricians" those terms were unheard. Most of the terms that have become standard now come from the industrial side where the guys making the drawings were those that learned terminology from going to college. In turn, those that taught the courses often were recruited from the current workforce and blended in some of the old terms with the more proper ones.

I had a discussion with my father a few days ago about a freezer that I have that is on the blink. He is 82 and sometimes forgets that I know anything at all. I explained to him that I checked the starting capacitor and relay. He then asked me if I checked the condenser. Condenser was used as a term for capacitor in the auto industry and ac motor field for a long time, still is but most people will give a blank stare if I call something a condenser. I used to know the history behind that term, but now it eludes me. My mind needs some cobwebs blown out.

Another leftover from the past is seen when you buy common house wiring. Two conductor with ground used to be known as three conductor. If you asked the clerk for three conductor wiring you will now get a four conductor, three hot wires and a ground.

I stated earlier in this tread that I had seen the solution to this puzzle somewhere in the past but could not remember exactly what it was. I have been trying to jog my memory and doodle on paper a bit to see what that might show. In trying to make a circuit, I see again what keeps it from being possible and do now remember more about the solution. You can't do it with just three SPDT switches. There was something more and it might have had to do with terminology.

I did come up with one configuration that works but you have to reset the breaker in one switch position. I don't think that counts.

A1 A2 A3 Y3 L1 C1 C2 C3 D3 L2 B1 B2 B3 Z3

L1 and L2 are the lamp terminals The Cs and Ds are common, the A,B,Y,Zs are common. The 3 switch is DPDT.

HOT-C1 A1-A3-Z3 B1-B3-Y3 C3-A2 D3-B2 C2-L1 NEU-L2

No. Open both ways in not the third item. It is called a three-way switch (for better or for worse) because it has three terminals.

Jerry

On Thu, 02 Nov 2006 14:57:44 -0600, snipped-for-privacy@grace.speakeasy.net (Matthew Russotto) proclaimed to the world:

The question asked was how to do this with three SPDT switches. There are several ways of doing it with different switches easily found in lots of different places, but you have to have at least one double pole switch.

Your reminiscence reminds me of a Saturday afternoon in 1946 when my father brought me to work. He was primarily there to let in the electrician who was to wire a large* shears, but busied himself with estimating a job, leaving me to wander through the shop on my own. The shears' size led its designer to power it with a motor at each end of the four-inch-diameter shaft that powered it, in order to limit shaft windup. Instead of the usual industrial motor starter with push buttons for on and off, this installation was controlled by a pair of relay starters to ensure that both motors operated together. The relays were operated in parallel by ordinary three-way residential light switches.

The electrician was directed to install a switch at each end of the behemoth. He soon returned to my father's office to say he was done. My father went to the shop floor and turned on the shears. Then he walked to the other, flipped the switch, and nothing happened: the switches were in parallel. He carefully explained that the motors had to go on from either end and off from either end -- that was the reason for having three switches.

Not long after, the electrician returned. My father flipped one of the switches and nothing happened: the switches were in series. Mt father explained again. The electrician got mad. "You can connect them either in parallel or in series. You can't do both!" My father got madder. He growled, "Let my kid show you." (I was 13.) One of my prouder moments! :-)

Here's another tricky switch use. The filaments of high-voltage gas rectifier tubes need to be fully warmed before the high voltage is applied. Unless a time delay is used, two switches are provided, and the operator know enough to wait. What they sometimes forget is, which switch is which. A fairly common amateur-radio practice used two DPDT switches so wired that either would turn on the filaments but both weer needed to turn on the plate supply. Clever, but not especially tricky.

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• It could cut ten-foot-wide quarter-inch-thick steel. That's LARGE!