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Three Light Switches and Three Lamps Challenge Math Problem

by JC, published: 2013-04-01 21:36 viewed: 226 times
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Here is another challenge math problem for gifted students in their 4th grade.

***

A little child was captured by some bad guys and put into a two-room jail. In one room there were only three light switches (nothing else!). and in the other room there were only three lamps (nothing else!).

There was one door leading from room to room. The bad guys said the child would be released if he could figure out which switch belonged to which lamp. But the child could pass through the doorway only once. (The lamps could not be seen from the other room. The child had to go through the doorway to see the lamps.)

Can you help him get out of jail?
Comments (3)
1. JC 2013-04-01 21:35
The same problem is described in other ways too. Here is a version with 3 light bulbs.

***

There are three light switches up in the attic of an old house... They control three light bulbs down in the basement. The problem is that you don't know which switch is connected to which bulb. You can make one trip down to the basement to figure this out.

How are you going to do it?
2. alan yuen 2014-11-05 18:53
I guess he is blind right?
3. JC 2014-11-23 23:45
Okey, let's see the answer now. The short answer is, turn on a switch and leave it on for a few minutes. Then, turn it off and turn on one of the others. The switch that is on corresponds to the lamp that's on, the lamp that's off but warm corresponds to the one that was first turned on.

Now here is a verbose analysis below.

Just think about the different possibilities. If we have all switches on, then when we go into the other room all the lamps will be on. This tells us nothing about which switch corresponds to which lamp. If we have 2 of the switches on, then when we go into the other room, 2 of the lamps will be on. This will tell us that the switch which is in an off position corresponds to the lamp that's off in the other room. And if we have 1 switch on (and the other 2 off), then we know which switch corresponds to the lamp that's on.

Neither of the last 2 solutions are complete – because they only tell us about one of the switches and the lamp that it corresponds to. But the problem clearly states that we need to know about all three of the switches, and which lamp each one corresponds to.

So it's now obvious that we must find some other way of solving the problem. Let’s think outside the box: what else do we know here? Well, the properties of a switch don't seem to have anything unique to them – they are just either simply on or off.

What happens to a lamp when turned on? Well, it gets hot when it is on, and warm after it is just turned off – so this is the 3rd observation that helps to solve the problem.
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