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 solution for 3 and 4 switches problem by Eugen)

Welcome to Perplexus!  We like to see new people around.  There is a very wide variety of puzzles here, and we hope you like at least some of them.

I'm sorry to say that this puzzle is not exactly a real world problem, and in retrospect, I should have said so in the problem.  If you read the rules, you may notice that there are a few big differences that defy the laws of physics.  I realize I could make some people very mad when I just do away with, for example, short circuits, but my purpose was to have people think about a new idea, not an old one.

I only allow a certain type of switch, and I am not sure that it matches the description of any of those in your link.  The end result (if you care to think about a non-real-world problem for long enough) is very elegant, though very complex.

That said, I liked your link--very interesting.

Posted by Tristan on 2005-06-09 16:15:29