Light Bulb Riddle

Here's another riddle. I heard it on Car Talk a couple of weeks ago, and I include it because the answer is elegant in the way that math problems sometimes are.

There is a long hallway, and down it, light bulbs hang from the ceiling. Many many light bulbs, the exact number doesn't matter, say 20,000 just for instance. These lights are all off. Then someone goes down the hall and pulls the chain on each bulb. The next person walks down and pulls every other chain starting with the second one. The next person pulls every third chain (the first chain he pulls is the third one). Then every fourth, fifth, etc.

The last person pulls every twenty thousandth bulb's chain. After all this happens, how can one predict which light bulbs will be left on?

Riddle, explained

There's a boy who comes to the Y everyday for several hours. He should be in seventh grade but was expelled. He's a nice enough kid: he plays chess, Scrabble, or speed with the staff when we're not busy, tries magic tricks, goes swimming, plays basketball, is completely bored after that.

I can almost hear him falling behind in school. Missing more material each day he isn't in class. Dropping behind in math, reading level, overall comprehension, motivation, hope of getting back on track.

I ask him why he doesn't bring a book to read for the hours that he has nothing to do. He says he doesn't read, apart from "How To" Origami books. If I brought in Hunger Games, I ask, would he at least read the first chapter? No.

He tells me that his mom writes him problems to figure out. If I write him a problem he would work on that. I wrote him the riddle that I posted here earlier.

My rule with riddles, which I inherited from my Dad, is that I will not tell anyone the answer. I will answer "yes" or "no" questions, I will give hints, but merely explaining a riddle takes away all of the joy to be found in it. (The joy of that "Ah ha!" moment. Joy, regardless of how many hints you've been given, of figuring out some part of it, of making the last intellectual leap.)

To a failing seventh-grader, I probably should have given a simple story problem.

The Teen Director came over to where the boy was working. Both were stumped by the riddle. TD took it back to the Youth Investment Staff, two men in their thirties, to try to work it out with them. One kept exclaiming that TD was "a four-point-oh college graduate" and should figure out the riddle, if the riddle were possible to figure out.

I told Mr. TD that it was the second in line who could figure it out. I asked him to think of what combination of hats could work for the riddle. I drew him a thought bubble of what the second could be thinking. (Sometimes it's hard to give hints without making the riddle more confusing.) I asked TD if the riddle was difficult or not. He realized the answer suddenly and told the other two. ("See, I told you, four-point-oh.")

The riddle itself is not that difficult; it just challenges our brains in a way we're not used to. I realized this when Mitch and I ate pizzas that night, and he was talking about teaching empathy. He taught a unit on AIDS that he said wasn't really to teach kids about medicine or health or to scare kids about sex. He said it was to challenge his students to see life from another's point of view. See concerns that are entirely not their own.

Because the trick of the riddle, the reason the second figure can know what color hat he has on his head, is that he both uses the information that he's given -- his experience, the hat that he sees in front of him -- and he thinks of what the person behind him must also see. He thinks from another point of view.

We, as humans, are terrible at this. From a survival, procreation standpoint, there is very little to be gained from empathy. But if it came more naturally, think of the footing that racism, sexism, classism, violence would lose.

And isn't that the point of reading fiction? Our good authors hold our hands, construct realities one detail at a time -- with clocks and food and dusty beds and list slippers -- to take us into the world of someone else. To make it a bit easier, for us, to see outside ourselves.

Riddle

Four men are lined up facing the same direction. One is behind a barrier and can't see anything in front of him. They can't look around. They know that there are four of them and in what position they are standing. They know that there are two black hats and two white hats, but they don't know who's wearing which hats (except for those they see in front of them). They are challenged to figure out which color hat is on their own head.
Once one of them figures it out, beyond a doubt, he will shout out that he knows an answer.

This challenge isn't really fair, though; it's only possible for one man to figure out which color hat is on his head. Which one is he, and how does he know?

*If you know, don't tell. Please.
**Credit for this riddle (as far as I know) goes to Kelly Vincent.