Cheryl's Birthday and Other Trick Maths Questions

So this went viral this week.

I hate these things. But I buckled down (at work!) and did it in 15 minutes. It helped to draw the dates as a matrix: months on the top, dates down the side.

The press spin is that 15 year-old kids in Singapore are smarter than almost everyone in the Western world. The excellence of Singaporean secondary education is a common trope of the western press, closely followed by the superiority of Chinese, Japanese and Korean secondary education.

Of course this is nonsense. For one thing, this superannuated grey-haired Anglo did it in about fifteen minutes. (I usually do the “Can you answer these GCSE questions” quizzes and I always ace them in a very short time though not after a couple of mis-steps along the way. The day I can’t ace them is the day I will apply for a job in product development.) For another, the exam board itself stated that this question was to help identify the better students.

And for another, this isn’t a serious question. It’s a trick. It’s the kind of trick question that a certain kind of epistemologist likes to use to discuss abstruse issues, and it’s the epistemological analogue of the trolley problem.

What makes a problem a mere trick instead of an interesting problem? An interesting problem gives rise to some theory to solve it: anything from an algorithm to a 400-page mathematical paper full of abstruse theorems. A trick is solved by a non-transferrable, non-generalisable argument. Remember all those integrals you had to solve at school? You had to play guess-the-substitution that would turn them into simple ones. Finding substitutions is a a trick. Integration by parts is a method, even if it does involve some trial-and-error.

Tricks give people the wrong idea about what a subject is about. The maths A-level syllabus used to be strong on tricks, whereas real mathematics is mostly about geometric insight to suggest theorems, and algebraic slog to prove them. Not finding a transformation or algebraic manipulation that magically makes the answer appear. Ask a serious chess-player whether they do chess puzzles: most of them don’t.

But the general public likes tricks. It likes to think that maths, or chess, or anything else that requires lots of reading, understanding, and actual insight, not to mention lots of trial and error, is really about seeing-something-that-makes-it-easy. Because that makes it magic, and the general public don’t mind not being able to do magic. Magic is, after all, just tricks. But if it’s hard work, and guessing and learning from mistakes, and adapting techniques you read about in some other contexts (that means reading, right?), then we’re looking at choices of how they spent as an adolescent, and now spend as an adult, their time and energy.

And guess what? Most people made choices that means they can’t solve a problem that bright 15-year olds in Singapore can solve.