The Weekly Warlock Wind-Up: Light bulbs

Those of you who were around for the very first Weekly Warlock Wind-Up (before it was even called that) nearly a year ago will remember that it was actually nothing more than a puzzle about light bulbs which I had come across in passing. And this week’s puzzle is exactly the same!

So, observe the set-up below. I have four light bulbs arranged with a switch in between each pair, and one bulb is turned on. When I flip a switch, it changes the states of the two light bulbs it is between i.e. if both adjacent bulbs are on, they will both turn off, and so on. My question is thus: is it possible to keep flipping switches so that all four bulbs are lit? If so, how, and if not, why not?

All will be illuminated on Friday…

Vel.

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3 Responses to “The Weekly Warlock Wind-Up: Light bulbs”

  1. Mishaweha Says:

    This sounds like a job for… state diagrams! *starts drawing*

    • Mishaweha Says:

      Far too many state diagrams. XD It became apparent, however, that they would form a cycle, and therefore there is NOT a way to get all four lightbulbs lit. After all, take a look at the initial state – you can either A) switch which lightbulb is on, which pretty much means the state didn’t change, or B) turn on two extra lightbulbs, which means you have the same as before, only now what’s on or off is revered. So if you have three lightbulbs on, the only two options are switch which one is off (option A, which means no change), or B) turn two lightbulbs off, which means we’re at the start again!

      There are a lot less state if you’re allowed to rotate them. 🙂


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