This is one of those tricks you just have to memorize and it's very hard to come up with the solution in 30 min.
What a great way to kick off a professional relationship:
"I know this problem is useless and obviously unrepresentative of the actual work we do. So do you (if you aren't incompetent). You also know perfectly well that I've memorized the answer and am only pretending to 'solve' it for you on the spot. And yet, we go along with the charade and pretend it's a vitally necessary, even clever hiring technique. Because hey, we're getting paid big bucks to play this game, after all. So who cares."
What a great way to kick off a professional relationship:
"I know this problem is useless and obviously unrepresentative of the actual work we do. So do you (if you aren't incompetent). You also know perfectly well that I've memorized the answer and am only pretending to 'solve' it for you on the spot. And yet, we go along with the charade and pretend it's a vitally necessary, even clever hiring technique. Because hey, we're getting paid big bucks to play this game, after all. So who cares."