House Arrest

Help Me Solve a Puzzle! January 14, 2011

Here is a puzzle for you mathematical and/or electrical people.

Harry has a basement room with two overhead lights in it. For some reason, these lights are not on the same switch.

One light, which we will call Tom, is a simple, easy-going light. It turns on and off with a single switch in the basement.

The other light, Cristobel, is more complicated. There is a separate switch in the basement AND at the top of the stairs. Either of these two switches will toggle Cristobel on and off (this is known as a three way switch).

Got it? One switch upstairs toggles Cristobel on and off. Two switches downstairs in the same box. One toggles Cristobel, the other toggles Tom.

Harry’s children are afraid of the dark. They also know they are supposed to turn off lights when they leave a room. When they go down to the basement, they turn on all the lights, but when they have finished playing in the basement, they forget to turn off Tom. They don’t touch the downstairs switches. They dutifully climb the stairs and turn off the switch at the top of the stairs. This turns off Cristobel, but it leaves Tom burning, sometimes for days, wasting electricity. No amount of reminders from Harry seems to stick, so that every time Harry walks downstairs to do laundry, he finds Tom burning and “PING” another hair on his head turns gray and falls off. Harry’s hair are an endangered species, and he would like to save what little remains.

So one day a new light bulb turned on, this time over Harry’s balding head. “What if I just rewire the switches in the downstairs box so both bulbs run off the same three way switch?” thought Harry. But after working on it for an hour, half of which was spent scratching his head and turning on and off breakers and carefully bending stiff wires with pliers, he has pretty much concluded it is impossible. At least, it is impossible only by rewiring the downstairs switch box. Actually, he would be happy if both Tom and Cristobel only toggle off the light switch at the top of the stairs, bypassing the downstairs switches completely. What he does NOT want to do is snake wires through the wall.

Is he right? Is it impossible?

Here are the details. There are five wires in the downstairs switch box: A, B, C, D, and E.

If the upstairs switch is flipped up, and you connect A and C, Cristobel turns on.
If the upstairs switch is flipped down, and you connect D and C, Cristobel turns on.
If you connect B and C, then Tom turns on no matter which way the upstairs switch is flipped.
No other combination will make a light go on.

The astute reading will observe that E apparently serves no function. I am guessing E is a ground wire, but I’m not sure. This is an old house with old wires all with black casing, and I’m not sure they did grounding back in the day.