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: Question by Tristan)

Ok, what about this?

A: PS = S1+
B: S1+ = LB
C: LB = S2+
D: S2+ = PS
E: PS = S3+
F: S3+ = PS

Now you've got two circuits, one that goes PS > A > S1+ > B > LB > C > S2+ > D > PS and one that goes PS > E > S3+ > F > PS. Does the light bulb turn on iff S1 and S2 are up, regardless of S3? Or if all three are up, the light bulb is off, but if S1 and S2 are up and S3 is down the light bulb is on?

Without some way to short-circuit the current from getting to the light bulb even if there exists a complete circuit, I am wondering if the problem is impossible. Even with short-circuiting, I haven't come up with a solution, but I have come close.

Posted by Avin on 2005-05-11 15:41:43