[MrRubix_MK5]

Guys, if the hands overlap, you know what time it is. How are you possibly going to get a different value for your hour and minute hands if they point to the same spot?

The kind of times you are looking for here are ones where the hands could literally represent two different times, even when you account for the fact that the hour hand moves along with the minute hand. What makes the riddle tricky is how you choose to deal with the angles involved, and how to reconcile the fact that different hours begin at different spots on the clock.