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Light Bulb Problem
You stand in front of a closed room in which there are three light bulbs. There are three switches on the wall in front of you: each of them enables or disables one of the light bulbs. You need to learn the relations between each switch and each light when you enter the room, because you can only once.
The status of the switches is random, and the order of the connection is not known beforehand. When you enter the room, you can do anything with lights, but you can not go back to the switches. Initially, all the lights are off.
Hint
If you want to solve the problem on your own, but there’s nothing coming to mind, you can use this hint:
Light bulbs have only two initial conditions: on or off. It is clear that this is not enough to divide them into three groups. You need to come up with another status for the lights and a way to achieve this status using the switches.
Solution
Logically, you can turn on one light and turn off the second one, but it is not clear what to do with the third. There are only two statuses for the lights: either “enabled” or “disabled.” The most popular way to solve this problem is to separate lamps using the “cold” or “hot” criteria.
First, you have to wait for some time to cool down the lamps in case that they have recently been working. Then, turn on one light to heat it. Turn it off and then turn on any other light. When you will enter the room after these operations, one lamp will be lighting the room, the second one will not be lit and will be cold, and the third one will not be lit and will be hot.
Now, it’s obvious that the one which is not lit and is hot is the one that you have turned on, heated and turned off, and the bulb that you have lit will be the one that you have just turned on, and the one which is not lit and is cold is the one that you never touched.
Another option is to add the status “burned out” if it is possible to apply a higher voltage than you need for the switch. Further action in this option is similar to the previous scheme.
As an extra, there is the idea to add the controller which will make the lamp blink to one of the switches. However, the most common way is described in the first solution.