3 light bulbs and 3 switches

This week's problem is a classic that's been around a long time ... but still a good one!

You are placed in a room that has 3 switches on the wall.  You are told that each switch controls a single light bulb in the room above you.  All 3 switches are in the "down" position, and you are told that all 3 bulbs in the room above you are currently off.  You need to determine which switch controls which bulb, but you are only permitted to enter the room above you ONCE.  How can you determine which switch goes with each bulb?

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SOLUTION FROM LAST WEEK:

The minimum number of races that you will need is seven.  Here's how you will do it ...

First of all, split the 25 racecars into 5 groups of 5 cars (since you can only race 5 at a time).  Let's now label each group as A, B, C, D, and E.

Each group will now race and the order the cars finish in will be assigned to each car as "A1" for the car that finished first, "A2" for second place, etc.  (Obviously group B will have "B1", "B2", etc., etc.).

After all 5 groups have raced, you now have completed 5 races.  You also know the fastest car in each group (A1, B1, C1, D1, and E1).

You will now conduct a 6th race involving those 5 "winners".  The winner of this race is your fastest car.  So far, so good ... 

But here comes the tricky part.  How do you determine the second and third fastest cars?  You can't simply take the top 3 cars from your 6th race, because there could be a faster car that didn't come in first in its original group.  To figure this out, let's look at an example.

Let's say that the order the cars finished in for the 6th race was as follows:  B1, A1, D1, E1, C1.  We know that B1 is the fastest car overall because it beat out the other 4 cars that were the fastest in their original group.  We also know that E1 and C1 are not going to be in the top 3 because they were beat by B1, A1, and D1.  We also know that cars E2-E5, and cars C2-C5 cannot be in the top 3 because they were slower than E1 and C1.

Ok, let's go deeper.  We also know that D2-D5 cannot be in the top 3 because D1, A1, and B1 are all faster.  Similarly, we can rule out A3-A5, because A2, A1, and B1 are all faster.  And finally, we can rule out B4 and B5 because B1, B2, and B3 are all faster.

This leaves us with only 5 cars that can contend for those remaining 2 spots in the top 3.  They are B2, B3, A1, A2, and D1.  Race these 5 cars in the 7th race and your first place finisher will be your second fastest car, while the second place finisher will be your third fastest car overall.