Here's a cool problem. I thought I came up with it, but it turns out it's been a Google/Microsoft interview question. The solution is pretty cool. Name all the times in a day when the minute hand is exactly opposite the hour hand of a clock. Or you could do the similar problem, name the times when the hands are on top of each other. And before anyone suggests moving this to the math forum, the reason I decided to put it here is that creative use of math is something that physics students need to practice and the guys in the math forum would tear through this with little benefit or amusement.