Answer to Riddle #7: Three Light Bulbs & Switches in a Room

7. A windowless room contains three identical light fixtures, each containing an identical light bulb or light globe. Each light is connected to one of three switches outside of the room. Each bulb is switched off at present. You are outside the room, and the door is closed. Before opening the door you may play around with the light switches as many times as you like. But once you've opened the door, you may no longer touch a switch. After this, you go into the room and examine the lights. How can you tell which switch goes to which light?

This puzzle is perhaps not as 'pure' as the others, it doesn't reduce to a mathematical model. But it is quite a common question so it's worth looking at quickly...

example of a three way switch Before reading the answer can I interest you in a clue?

The consensus of opinion seems to be this is the best answer:
• Switch on switches 1 & 2, wait a moment and switch off number 2.
• Enter the room. Whichever bulb is on is wired to switch 1, whichever is off and hot is wired to switch number 2, and the third is wired to switch 3.
Obviously any combination would work. It doesn't have to be switches 1 & 2 you flick, any two will be fine, so long as you can remember which. There is another possible answer, this involves switching on 1, then waiting a while and switching on 2. When you get in to the room two of the bulbs will be on but one will be much hotter. It's valid, but there are several reasons why this is not as good. I have built below a sort of simulator. Have a play, it's obviously more of a test if you hide the Bulbs until you've finished messing with the switches!

Note: no information is sent to me, the simulation is done entirely locally, on your computer.
a bulb switched on a bulb switched off a bulb just switched off

Alternative form with one bulb.

Another form of this puzzle sets up that you are renovating a building or something like that. There are three switches in the basement, two of which are useless, one is connected to a lightbulb in the attic. You must determine which needs saving and remove the other two. It's basically the same solution as our first idea. That is switch on 1&2, wait a minute, switch off two and go to the attic and check if the bulb is on, hot, or cold.

As I say this puzzle is unusual for this site in that it is not completely pure, it's pragmatic rather than pure logic. But it is a very common question and that earns it it's place.







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