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 Challenge for Tristan by Mindrod)

Well, it has been about 6 months since this was posted (and 9 months since I wrote it), and it doesn't look like anyone is about to solve this.  How about this--I'll show the first half of the solution.




***Spoiler to 3-switch problem below***






Solution for three switches and one power source:

P1 connects to wires A, B, C.
LB connects to wires D, E, F.

Switch   Position 1   Position 2
1        A,D,H,J      B,G,E
2        F,H,I        G,C,J
3        E,A,I        D,B

I can absolutely guarantee that this solution follows all the rules.  I've checked it very thoroughly many many times.

If you think the solution looks wrong, you are missing something.  Note that there must be two disjoint paths from the power source to the lightbulb.  If switch 1 and 3 are both in position 1, there are two paths: P1-A-D-LB and P1-A-E-LB, but they are not disjoint; they both use wire A.

Posted by Tristan on 2005-11-25 22:02:23