I’d explain the title of this post, but you already know what I’m talking about. I refer to questions like this one, from the 4th century:
I, for one, pity old Demochares—enumerating the fractions of his life, yet unable to recall his own age. It’s a bizarre, selective senility, like something from an Oliver Sacks book: “The Man Who Mistook His Life for a Math Problem.”
Or consider this problem, from the 21st century:
Over the last three millennia, much has changed. Civilizations have risen, collided, and fallen. Revolutions have left legacies in blood and ink. There have been, for good and for ill, 417 million Marvel films. Yet somehow, these age-based math puzzles have remained a constant.
What’s the case for them?
Well, they’re easy to state and tricky to solve. They take a naked mathematical structure and give it a fig leaf of narrative—just enough to require some imaginative effort. They’re a convenient variant on an algebraic theme.
And the case against them?
Well, they’re artificial. If you’re presenting such a problem to a pupil or a pal, then you’d better hope they’re already invested in the project of mathematical puzzle-solving. If not, a stilted find-my-age puzzle ain’t gonna reel them in.
I recently came across a “real-life” (well… “fictional-life”) instance of such a problem on the first page of Lolita, Vladimir Nabokov’s classic novel about a child predator who becomes infatuated with a twelve-year-old girl:
In point of fact, there might have been no Lolita at all had I not loved, one summer, an initial girl-child. In a princedom by the sea. Oh when? About as many years before Lolita was born as my age was that summer. You can always count on a murderer for a fancy prose style.
For what it’s worth, our narrator does not give quite enough information to determine the age gap. (You can count on a murderer for an under-determined system of equations.) But a few additional facts—for example, that he was 13 years old that initial summer, and 37 upon meeting Lolita—suffice to fill in the gaps. (The composition and solution of such ghastly problems is left as an exercise for the novel’s reader.)
Should we forswear such problems as carrying the ineradicable stain of Nabokov’s protagonist? Or embrace them as carrying the indisputable glow of Nabokov’s prose?
Cards on the table: I’ve rarely used such problems in my own teaching, though I have nothing against them on principle (icky Lolita associations notwithstanding). My own taste is towards heightening the weirdness and trying to nudge them towards a more open-ended form. Something like this:
Do these have the same spirit as the classics that open this post? Not really. But then again, those two openers don’t have quite the same structure, either. Love ’em or hate ’em, these age problems will stick around because they’re convenient hooks for hanging all kinds of algebra on.
What say you, my fellow jurors?
NOTE: I’ve made a few edits because people weren’t loving this post’s winning combination of jokey unhelpfulness and pedophilia references. I can’t imagine why!