Puzzle 1: Obviously, you must set the switch to "ON" and then check the status of the light. If it's not on, the switch is broken.
Puzzle 2: To solve this puzzle, set one switch #1 "ON" and switch #2 "OFF". If the light is on, then it must be controlled by switch #1. If it is off, we assume it is controlled by switch #2.
Puzzle 3: One obstacle to solving this problem is to believe too strongly in abstraction. An abstract light bulb is either off or on, and has no "memory" of its previous state. But we know that's not true in real life. A light bulb that was recently on and is now off is quite different from one that's been off for a long time - it's still warm.
So to tell which switch is which, you turn on switch number 2 for a few minutes. Then you turn switch 2 off, and turn switch 1 on. Now you go immediately to the room with the light bulb. If the lightbulb is:
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.
Since lightbulbs also take a certain amount of time to warm up, you could theoretically use a variation of this method to solve a similar problem with 4 switches.
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