Of course, in no time a riddle was served along with dessert. It went something like this: There are 100 switches in a row (don’t ask switches to what — widgets, turbines, whatever), and they are all in the “off” position. Now you go down the row and turn every second switch “on” beginning with the first. Then you go back to the beginning and flip every third switch, turning it “on” if it was “off” and vice versa. You go on to do this with every fourth, then every fifth switch until you do every 100th, and the question is how many in the end are “on” or “off.”

Now, I love riddles of a different kind as I will explain, but this riddle was causing me a headache even as it was being delivered; I did not even try to think about a solution. My youngest son, who seems to share my aversion for all things mathematical, looked as anxious as I did. What surprised me was how engaged we all were, despite ourselves, by this problem that had no basis in our experience — the riddle took root and held us.

The kinds of riddles I like are medical riddles, which are a different beast. In fact, I vote not to call the widget-switch thing a riddle. Call it math in camouflage. And the same goes for the riddles that have to do with puns, as in, “Why did the doctor give up his practice?” (“Because he lost his patience!”) So also for the cute definitions, as in, “The man who made it did not want it; the man who bought it did not use it; the man who used it did not know it. What is it?” The answer is a coffin. (I mean, really!)

My kind of puzzle

By medical riddle, I mean the variety that instructs, that forces a student to reason, to make some hypothesis, then stimulates them to go to the books and do more research and eliminate this or that. Those kinds of riddles have a special place in medicine, because they are part of our legacy, handed down carefully. They also make you think — in the purest sense of the word. How long has it been since you just sat there, the door closed, the computer turned off, your iPod silenced and you did nothing but think about a problem?

As a student, I learned from trying to solve these riddles, and now I collect them. Here is an example: I might ask a student on rounds, “Why do we say, ‘Beware of the patient with a glass eye and a big liver?’” (And I hasten to tell them that I don’t want an answer right away; these simply are not those kinds of riddles.)

What I want is for a student to reason this out. The steps ideally might go something like this (the italics represent the inner dialogue).

I wonder why the patient has a glass eye to begin with. What caused that?

I suppose it could be trauma . . . could be a malignancy. Let me look up the causes.

In looking up common diseases that cause the eye to be removed, the student might realize that people with malignancies that occur in the eye often undergo this treatment.

Hmmm, a melanoma in the eye is a common reason to remove an eye. (Or used to be — it has changed a bit with new treatment.)

Now . . . how would that connect to a big liver? Hmmm. If melanoma metastasized to the liver, then they probably would never have taken the eye out in the first place and replaced it with a prosthetic eye.

At this point, the student might look in a textbook or an online resource, like UpToDate, and find that ocular melanoma is famous for recurring years later with distant metastases. When it does return, it often presents with new tumors in the liver. Bingo! Riddle solved and something learned along the way.

Resist temptation

Alas, there is a new wrinkle to this issue, one that professors of medicine of old did not anticipate: If the student decides to google the question by typing in “glass eye and big liver” as I just did, the first hit is NEJM: Solution to a Medical Mystery, which gives the answer to a 1997 New England Journal of Medicine photoquiz that asked essentially the same question as our riddle. A total of 928 readers had the correct answer. No surprise, because it’s an old riddle.

Since ancient times, riddles have served as teaching tools. And this is why when I offered a new riddle to my newest batch of students as we were making rounds this week, I said, “Don’t google!” Now, I have nothing at all against Google — indeed my kid brother works there. But the point of the riddle, at least the medical riddle, is to search your brain, then search your books or the library, then connect the dots. To reason and to come to the answer for the right reasons is wonderful. You don’t want to google. (Unless it’s one of those 100-switches-in-the-off-position riddles, in which case I say, go for it.)

In case you’re curious, this is the riddle I gave my students and which they are supposed to report on this week:

A man walks into a bar and offers to keep his head completely submerged in a bucket of water for 20 minutes. If he doesn’t, he will buy drinks all around, and if he does, the patrons must stand him a round of drinks. He does and so they do. The question is, how did he do it?

Before you ask, I should tell you there is no hidden tracheostomy, in other words, no artificially made opening from his windpipe. And yes, his head is truly immersed in the bucket, and there is water in the bucket — and it’s in liquid form.

This is one that requires some thought. But no math to be invoked, no cute puns to be discovered. Just thought, then research, then more thought. And remember, don’t google this riddle!

 

For the answer to the riddle click on "Solution" in the right navigation menu.