Here is a puzzle that illustrates the difference between mathematics and reality. I had convinced myself there was no solution, and was preparing to prove it, when I realized what to do.
You are downstairs in the living room. There is a light switch on the wall, labeled "ON" and "OFF". This light switch should be connected to a lamp upstairs, in a room you can't see. It is possible the connection has been broken. How should you set the light switch so that once you get upstairs, you will know whether the connection is good or not?
OK, so you're back downstairs again, but now there are TWO light switches on the wall. One is definitely connected to that lamp upstairs, and one is not. How should you set the light switches so that once you get upstairs, you will know which switch is connected to the lamp?
Now here's the hard part. You're back downstairs yet again, but now there are THREE light switches on the wall. One is connected to the lamp upstairs, and two are not. How should you set the light switches so that once you get upstairs, you will know which switch is connected to the lamp?
(While you're at it, could you handle FOUR switches?)
I give up, show me the solution.
Back to the puzzle page.