Brain Teasers Involving Time and Watches

I teach high school math. This year I am going to start my classes with a quick brain teaser. My students seem to like it so far. What ideas do you have for brain teasers involving clocks, time, and watches? Who knows, maybe some of them will even learn to read an analog clock.

For example. I had them list all of the times when the hour and minute hand overlap on a clock. It got them thinking.

Thank you.