You have two tasks. You must design a 3-switch lamp and a 4-switch lamp. It is recommended that you try the 3-switch lamp first. Your design will include a lightbulb, wires, switches and power sources. The design must follow these rules:

1. You may only use 1 lightbulb for each lamp. The 3-switch lamp can only have one power source, and the 4-switch lamp must have exactly two. You may use any number of wires.
2. Every flip of a switch, no matter the previous positions, must turn the lamp from on to off or off to on.
3. Each wire may connect to any number of switches, power sources, and other wires, and to the lightbulb.
4. Each switch has two separate positions to which wires can connect. If the switch is up, then all the wires connected to position 1 are considered connected to each other. If the switch is down, all the wires connected to position 2 are considered connected to each other.
5. The lightbulb turns on if and only if there exists a complete circuit that includes both the lightbulb and at least one power source.
6. A circuit is a sequence of wires, power sources, and the lightbulb where each is connected to the next item in the sequence (the last is connected to the first). No such sequence may list the same wire, power source, or the lightbulb twice.

I recommend that you denote the different wires with letters like A, B, C, etc.

(In reply to re(2): AAAAAAAAAAAAAAARGH! by Avin)

The inverse of the 4 switch problem sounds interesting.  I might look into it later.

One of the most difficult parts of writing a puzzle is choosing a way to explain it.  I have to find a perfect analogy.  Ideally, the analogy should sound simple, and not contrived.  This way, the puzzle as well as the solution seem more elegant.  For this puzzle, choosing a good analogy is particularly difficult.  If I were to write this puzzle over again, I would completely avoid any reference to electrical circuits.  I think I would analogize it to people instead of wires, kind of like the Conversing Club series.  I could add some sort of sci-fi element, like, I don't know, telepathy.  There's probably a way.

The fact that there are so many solved puzzles without official solutions is probably our (the voters') fault.  We neglect the solution queue a whole lot.  The solution queue is huge.  Scary, really.

Posted by Tristan on 2006-01-24 13:33:17