The Role of Riddles

I came across this riddle and it got me thinking:

First of all, the premise of a logic rave at “Learning Man” is just adorable. And I wished that more kids could be exposed to it.

Then I realized all of the challenges. How would I teach this in a classroom? Clearly, I should outline the problem. But then I would need to give the kids some time to think about it? How much time?

If you watch the video through, you’ll see that the solution requires a small flash of insight; a way of approaching the problem that unlocks it. How long would it take someone to come up with that? Clearly some people are simply incapable of it and would never come up with it. In that case, forcing them to think about it would amount to extended mild child abuse. I encountered a problem similarly where a teacher proposed a riddle of this form and didn’t give us the answer. I had a dentist appointment during the following class and consequently missed the explanation. Too embarrassed to ask, I let it slide. I thought about it from time to time, but ultimately, I had to wait nearly fifteen years to come across the riddle in a YouTube video like this one to find the answer.

So I started to understand why this wouldn’t find its way into a math class. First of all, the solution is oddly specific. It’s specific to this problem (the demon giving very little, but carefully selected bits of information) and it’s unclear how this strategy generalizes to a broader class of problem (what’s the real-word analogy of being let in a gate based on the colour of a mask you can’t see?) but also specific to the number of logicians. If there were one more or one fewer person involved, the solution wouldn’t work. Then I recall that I explain this to tutoring students all the time. In math we prefer methods of solving problems that are robust: they have to keep working even if the numbers get difficult — too large to count on the fingers, or ugly fractions or decimals. That’s why we avoid solutions based on the strategy of “guess and check” as much as possible.

I wonder if there is a way to incorporate problems like this. On the one hand, it expresses one of the fundamental principles of math in a fun way: that you can extract a lot more than you expect from very limited information. But they seem to have intrinsic time wasting properties that don’t fit with the timetable of modern school.

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