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 Trying to build on the 3-switch solution... by Avin)

I'm happy to see that at least one person has kept this problem on the watch list.  Thanks for the improved 3-switch solution--I'll credit you in the official solution.  I'm rooting for you on the 4-switch problem.

As you might guess, this was one of my more ambitious puzzles, if not the most ambitious.  This sort of puzzle is very fun and challenging to write. Unfortunately, it is also very challenging to find a proper wording, and the difficulty level can be riskily high.

If this one is solved, I promise to make a diagram.  Good luck!

Posted by Tristan on 2006-01-20 01:51:06