[Taken from Thinking Mathematically, p. 163]
When my son was born, my wife and I agreed that if he woke up before 5 a.m., she would go and feed him, but after 5 a.m. I was to go and bring him into our bed. One night when he woke up, my wife looked at the clock in the dark and said it was my turn. Surprised, since it seemed rather dark, I nevertheless acqueiesed. Later, it turned out that my wife had looked at the clock upside down and mistaken 12:30 for 6:00.
When will the hands of an updside down clock show a proper clock time?