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 the first case - the drawing by pcbouhid)

I think you're misreading Tristan's puzzle--standard 3-way and 4-way switches are not allowed.

Per rule #4, the switch boxes have two posistions and two nodes to connect wires to.  When you switch to position 1, then all the wires connected to node 1 get connected to each other.  When you switch to position 2, the wires at 1 get disconnected from each other and all the wires atached to node 2 get connected to each other.

Think of it a a multi position knife switch like this one (http://www.herbach.com/Merchant2/graphics/00000001/swh2540.jpg) only with an arbitrary number of connections at either side.  You still only get to connect either all the wires at one side or all the wires on the other side.

The switch in the picture is a double pole double throw (DPDT), Tristan's switchs are double pole n throw (where n is some arbitrary number).

Posted by Erik O. on 2005-05-09 22:08:25