Toggling between two lights with two separate SPDTs

[just4user]

One of the lights should always be on and never two. It's easy with a single SPDT, but is it possible at all with two? (So that toggling each switch swaps the light that's on.) I can also do it with two DPDTs, but not two SPDTs. It's for AC mains, so no other fancy elements need to be involved.
Here's the closest I've got: https://www.falstad.com/circuit/circuitjs.html?ctz=CQAgjCAMB0l3BWcMBMcUHYMGZIA4UA2ATmIxABZsQkFIaBTAWjDACgBlEbBFEFCvSp8B9MSABmAQwA2AZwZR+bAG7gUeboU1gN-DH3oRBNJWOgI2YPBEIJC4DA7sPMh7pATQsBvBgpgFBr2yEZoUNAUERRWNiAu3HhRCRR44rgweISEGKQoYAhZCBBgcOrmUTAxAO7cvPwmuppuUGy1wvwC8SFgTq1c2NqU2HwUqcPuENLyivQobRP8IYOaHZALCb0OY6tgDuvt4zvdDthJrbVNWpoJLQfqmiuU47ya98evJ5RprUA
But notice that if the lower switch is up, then the upper switch's position won't matter. 

[Andy Chee]

Like this?

https://www.falstad.com/circuit/circuitjs.html?ctz=CQAgjCAMB0l3BWcMBMcUHYMGZIA4UA2ATmIxABZsQkFIaBTAWjDACgBlENPbi+lHl4p+UcCABmAQwA2AZwZiUbAG7hBIbIV5gNmFGIiik9U9ARsweIxWEYDFW5q1jchaNgz88FQiiIYeMQUyPS6ZiEwFJbWzoTc9nFJ9Lgo5hiQgaRYxHi4SGBw6hFQ0NFcPJo+3EJVkeLS8ooCbADu6nYGusKikG0dfAL4g1D93ZraA9jVfe3j0yGVC6PtgsII8dguKBsrSTub24mzNbxaZy7ne1ubkzfJ-WvcIpRO-pH9jsIvXwkGJ797r9+KZPk4QadKEU+kA

[just4user]

One of the lights should always be on and never two. 

[Ian.M]

No.  You need one SPDT to make an initial selection between two lamps, and one DPDT wired as a crossover to swap the lamps.

https://www.falstad.com/circuit/circuitjs.html?ctz=CQAgjCAMB0l3BWcMBMcUHYMGZIA4UA2ATmIxABZsQkFIaBTAWjDACgBlEPelC+sIV78oogGYBDADYBnBqJRsAbt3r96PEH3oDK9JDqjQEbMHggUKeLRhSUrew7jzQMYYiRQowkPnZ8CaEYUwabmINjYhDZ2kdHqorgCcOBBMCHpbADu4EJaCNHudigFUNlaeNaYsVExZTkoleDEdpbWRfX27S1ddZDlbY4RtQn9VAI9aFUiU6L0krIM5YK8fM3F+J2aCXFD-UA

[just4user]

Just because you can't solve it doesn't prove what I'm asking is impossible, but thanks for the alternative 🙏
I think it's only credible to prove its impossibility by exhaustion, i.e. writing a python script that goes through all possible connections between the main elements to see if any configuration can satisfy the requirements.

[BeBuLamar]

You need to turn both off some of the time? Or you always have one on?

[themadhippy]

is  a link between the switches that mechanicaly interlocks them allowed?

[MK14]

You can almost/partly/somewhat do it, by (partly cheating).

In the following circuit (using a shortened URL link), and messing with the bulbs wattage's, such that, one (when on) glows brighter than the other.
E.g. Something like 150 watts for one bulb, and 25 watts for the other.

https://tinyurl.com/28263m83

I.e. Either the first is on, as normal, or they are both 'on', except that because they are now both in series, the considerably lower wattage bulb, will glow brightly and the much higher wattage bulb will appear to be off, as the current flow, will be too low to light it, if suitable wattage's are chosen.

EDIT:
Or another alternative, is to use an incandescent bulb for the high wattage one (in the circuit I linked to), perhaps 60 or 100 watts and a much lower power consumption LED one, as the lower wattage one, perhaps 6 watts (LED).  I think that would work, and the lights could then look similar and be similar brightness levels.

[just4user]

@UHF
If you can formally represent it with logic gates, by all means...
It may look like a XOR, but I don't think it's that simple since as I said in the beginning, it's easy with a single SPDT, but not two.
I think graph theory may be more appropriate to prove it's impossible in this scenario.

@Everyone else
Ian understood the problem. Just check the link to his circuit.

[IanB]

It's not possible with just two SPDT switches.

[just4user]

Prove it.

[golden_labels]

Is this a homework? The way you react seems like making demands one doesn’t make while actually asking for advice (requiring proofs), or like being confrontational against those trying to help you.

In terms of absolute logic you’d be right, that not being able to show a solution doesn’t make the solution impossible. But you are completely wrong in the assumption, that exhaustive search is needed. The problem statement is itself equivalent to a binary logic equation, and usually exhaustive search isn’t needed to show such an equation has no representation consisting only of given elements.⁽¹⁾ Furthermore, asking for advice is seeking an opinion from a more experienced/knowledgeable person, implicitly putting trust in their judgement. It’s probabilistic, not binary-logical.

So what’s your goal? If you demand from other people to put effort into creating a proof, where is your effort? What’s your proof showing it’s reasonable to think there exists a solution? If you believe only exhaustive search could prove that, why do you expect others to do it instead of you? The problem space is tiny in this case.

⁽¹⁾ For example this is how we know XOR alone isn’t functionally complete. Despite it’s impossible to exhaustively test that statement.

[just4user]

You guys love to chit chat. I hate it. I wish the "Super Contributor" tag meant something, other than someone who posts what has already been said whenever he gets the chance

[Andy Chee]

I might as well hijack this thread....

I remember in the puzzle section of an electronics magazine a similar in theme, but not exactly the same, globe switching problem.  One contributor submitted an out of the box solution that involved a return path via earth instead of neutral!

[artag]

You guys love to chit chat. I hate it. I wish the "Super Contributor" tag meant something, other than someone who posts what has already been said whenever he gets the chance

It's a chat forum, a community, not a textbook. If we just wanted to answer and be rated, we'd be in the stack overflow hell.
So yes, we love to chit chat. Self-selection.
I'd agree though that 'super contributor' would be more useful as an indication of number of 'thanks' rather than posts.

[SteveThackery]

You guys love to chit chat. I hate it.

God, how rude are you? I can tell you are young because your brain hasn't learned how to deal with people yet. There's this thing called "politeness" - you should look it up some time.

But know that nobody owes you anything: an answer, an explanation, or anything else.

I suggest you clear off now and come back when you're an adult.

[Ian.M]

I assert that my solution above (#3) is minimal, subject to the requirements that the lamps are identical and lamps that are off must have negligible current through them.

Reasoning: a SPDT contact set can distribute one source to two loads or select one of two sources to feed a load.
Multiway lighting circuits (i.e. to switch one light from two locations with neither having priority) are well understood: https://en.wikipedia.org/wiki/Multiway_switching
It is obvious that the minimum to control a single light from two locations is two SPDT switches.   The O.P.'s problem is to control two lights in opposition so that one and only one is always on.  This can trivially be done by two minimal circuits of two SPDT switches, ganged in pairs as effectively DPDT switches.  However there is an obvious shared minimisation - the switches at the supply end of both circuits perform an identical function so can be combined as a single SPDT switch, giving my one SPDT, one DPDT switch solution.

The DPDT crossover switch at the load end cannot be minimised, as it must swap two sources (the complimentary feeds from the SPDT switch) between two loads.

Considering alternatives: The topology of two lamps in series across the supply, with the center point switched to either side of the supply obviously provides the complimentary function from a single SPDT switch, but there is no way to add more SPDT switches without one having priority (i.e. preventing one or more other switches from controlling the lamps), so a DPDT is require to reverse the supply connections to the SPDT. 
https://www.falstad.com/circuit/circuitjs.html?ctz=CQAgjCAMB0l3BWcMBMcUHYMGZIA4UA2ATmIxABZsQkFIaBTAWjDACgA3EPeiub+mAyEo4SvST0p0BGzB4I2bCKEilIlHjyjcg-mDRRoFIxTkKQ6kJu1W+Uy5GwzsKVtlZhCBDEjD7DGBMgtgB3cE1wYQjtFAQRSDCYqLVlFKgkg217ZKtE8LRbQxQ+R2DMyJy7fnzrfGsMFGtSzCbEgGUy6y1m+htRCAAzAEMAGwBnBlEUNio++tdBaMXRehGJhiSedKz02u2c3Zza3BN+q37EoA

Most (I believe all) alternatives can be reduced to one of the two afore-mentioned circuits by trivially re-ordering the switches, lamps and supplies in each series loop.

Prove *ME* wrong, if you can!

[Zero999]

Add a DPDT relay and it's easy.

This is my first and final post to this troll thread. Reported to moderator. Over and out.

[MK14]

Prove *ME* wrong, if you can!

I have, because my solution works just fine (in theory, I haven't tried it, it may not work when tried?) with a pair of single pole, double throw switches.  As long as you can live with mixing LED and incandescent bulbs.

[Ian.M]

Prove *ME* wrong, if you can!

I have, because my solution works just fine (in theory, I haven't tried it, it may not work when tried?) with a pair of single pole, double throw switches.  As long as you can live with mixing LED and incandescent bulbs.

Yes, if you move the goalposts, you open up new solution spaces.  That's why I specifically said

I assert that my solution above (#3) is minimal, subject to the requirements that the lamps are identicall and lamps that are off must have negligible current through them.

to exclude solutions similar to your reply #7, which is admittedly a clever hack.

The idea was to put the onus on the O.P. to prove me wrong rather than acceding to their demand for everyone else to prove themselves right!

[MK14]

Prove *ME* wrong, if you can!

I have, because my solution works just fine (in theory, I haven't tried it, it may not work when tried?) with a pair of single pole, double throw switches.  As long as you can live with mixing LED and incandescent bulbs.

Yes, if you move the goalposts, you open up new solution spaces.  That's why I specifically said

I assert that my solution above (#3) is minimal, subject to the requirements that the lamps are identicall and lamps that are off must have negligible current through them.

to exclude solutions similar to your reply #7, which is admittedly a clever hack.

The idea was to put the onus on the O.P. to prove me wrong rather than acceding to their demand for everyone else to prove themselves right!

Yes, you're right.  I didn't notice, those parts of your post.  I mainly read the initial claim, and made my response(s), as a result.

In some cases, (in real life), I suspect there are SPST switches, already installed.  But because it is of historic importance and/or sentimental value and/or you don't have 'ownership rights/permission' to change the switches and/or the switches are outside your field of influence (e.g. shared apartment hallways, but one or more of the lights, is in your apartment, or at least partly lights it), etc.

So, there can be a need for crafty solutions, to problems, like the one in this thread.