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Here's an easy puzzle that should take you only five minutes to solve, inspired by my hallway. Most intuitive answer get the mark:

Six switches control the same light bulb in a multiway switching scheme. That way, changing the state of any switches changes the state of the light bulb.

In the beginning, all six switches are at the UP position and the light is on. How do you turn the light off and have all six switches at the DOWN position?

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    $\begingroup$ Given the correct answer, I guess the tag lateral-thinking should be applied and not to be removed. $\endgroup$ – athin Apr 14 '20 at 3:02
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This is

Mathematically impossible, as there are an even amount of switches that all need to be switched, and only an odd number of switches will lead to the light being off. As no number is both even and odd, it cannot be done mathematically.

However

That doesn’t mean the conditions can’t be met if we think laterally.

As light switches are symmetrical, switch 5 to down, so the light is off, unscrew the last light switch, turn it 180 degrees and screw it back in! Now all light switches are down and the light is off.

enter image description here

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I believe that the most intuitive answer is that

...you turn the light off by disconnecting the bulb.

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  • $\begingroup$ Or at the fuse box... $\endgroup$ – Chronocidal Apr 14 '20 at 11:58
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With Lateral Thinking I can do this by

Turn the relevant circuit breaker off on my electrical panel (or even the main circuit breaker switch off) and then have all switches in down position

That works for me. :)

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Toggle 5 of the switches immediately off, and stop paying your electic bill. Wait right until you get a final notice from your electric company for not paying your bill, then toggle the final switch. Within a few days, the light will be off.

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Not a legit answer since it's not definitive and not a "Puzzle" solution you can logic out, but...

6 switches is going to be difficult to implement in the same way they implement a 3-way. If you really HAD to do it with wires and multi-pole switches (6 pole two throw?), the switches would be quite expensive and rare and you'd be running a pretty big bundle of wires between them.

However a solution involving relays and/or software would be much more likely to be used in an implementation that big. It would probably trigger on edges rather than track the state of the switches.

Assuming the later implementation, I'd try flipping 2 at the exact same time to try to "Trick" the relay (or software) into firing only once and changing from even-on to odd-on.

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Strictly speaking, it'll take an even number of changes to make all the switches DOWN so light will be on. But if it's allowed to operate multiple switches at the same time then you can turn first two switches DOWN at the same time. Light will be off and states will be 2 DOWN, 4 UP. After that you switch other 4 down one by one so that all the six are DOWN and light is still on.

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  • $\begingroup$ That is... not how multiway switching lights work. It's not the event of changing the switches that determines if the light is on, it's the current state of the switches. So when you flip two switches - even if you could perfectly time them to flip at precisely the same time, the result would be the light stays on. $\endgroup$ – Darrel Hoffman Apr 14 '20 at 13:39
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You need rotary light switches with 3 or 4 positions for ON/OFF (https://i.stack.imgur.com/m8gtF.jpg)

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