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): Question by Avin)

As it is written, the puzzle ignores the possibility of short circuiting.  Looking back at my solution, it is destroyed by short circuiting.  I apologize for not being very faithful to reality, but to solve this puzzle, I'm afraid you're going to have to accept the contrived rules I wrote.  That's what happens when I try to make an elegant and difficult puzzle from a complicated set of rules.  Most sets of rules I tried were either impossible or trivial, and if I changed the rules again, it might not work out right.

It has come to my attention that some people might think that both the power source and light bulbs are connected to the "ground" or something like that.  This is not the case.  For a circuit to exist under these rules, there must be two disjoint routes from lightbulb to battery.

Now, for a summary of how the rules differ from reality:

Batteries have no negative/positive ends to restrict flow of electricity to either direction.
No short circuiting is possible; if any circuit exists, the light turns on regardless of other circuits excluding the lightbulb.
A circuit may go through (list) a switch junction more than once.
The light bulb and power sources do not necessarily connect to the ground.

Some of the above differences are important, some are not.

Now, honestly, I don't take physics electricity and magnetism class until next year.  Perhaps I should have written the puzzle with a different theme, so my rules wouldn't conflict with preexisting knowledge of how electricity actually works.

Posted by Tristan on 2005-05-11 23:33:21