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 Model for 3 switch lamp by brianjn)

I am absolutely sure my solution works, under the rules given.  You must remember, as I have already stated over and over again, that this is not a real world problem, as the rules are not the same.  Using the real world rules would probably make this impossible.

One of the main things that may help you and others, is knowing that under these rules, the lightbulb and battery need two connections to make a circuit.  A wire connecting the lightbulb to the power source only makes half a circuit.  Assuming the other half of the circuit is already there by default will lead to problems.  Both halves of the circuit will go through the switches.

Posted by Tristan on 2005-06-30 21:53:46