Thursday, December 29, 2011

Three Switches and Three Blub Problem

Problem

You are standing outside a room next to three switches, all of which are off. Each switch operates a different light bulb in the room. The room door is closed, so you cannot see which switch operates which bulb. You are only allowed to go into the room once. Determine which switch operates which bulb.

Solution

Stumped? The issue lies in the fact that there are only two possible positions for each switch (on or off), but three bulbs to identify. Identifying one bulb is super easy, just set one switch on and then go into the room to check which one is on. But then, how do we detect the other two?

So let’s think deeper, what are the other properties of a light bulb operated by a switch? Light bulbs definitely produce light, but they also produce heat (a not so very important characteristic!). Any chance we can use this idea to help solve our problem? Since a light bulb would take sometime to lose its heat after being switched off, you could still determine if it had ever been on by touching it.

So now, we can easily determine which bulb is operated by which switch.
Lets denote switches by A, B, C
  • First, we turn the switch A on and leave the other two off. 
  • After 5 minutes, we turn the switch A off, turn switch B on and leave the third switch off. 
Now, we have
The hot bulb is A
The lit bulb is B
The dark bulb is C

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