When I was in 10th grade, our school had a monthly math competition of some sort. To this day, some 20 years later, I can recall a question that baffled me then, and, on the occasions since then when I have had time to think about it, continues to baffle me now. I’m sure that some of you will make short work of it, and perhaps allow me to reallocate the mental real estate it occupies to something more useful, like the birthdates of my children.

The question is simple: when a clock is set at 12:00.00, the hour, minute, and second hands are all precisely aligned atop each other. At what time will this condition occur again?

(Obviously, the problem can be solved by trial and error, but the test required a mathematical way of solving it, so I’m looking for an equation or set of equations.)

Ready? Begin.