This one may have been posted already but here it goes:
An extraordinary man constructed a special clock where the hour hand and minute hand were identical. It was hard to tell the time when one looked at this clock, but the old man claimed that it is usually straightforward to interpret the positions of hands. For example, at 5:00, when one hand points to 12 and the other to 5, there is only one possible interpretation: if the hour hand pointed to 12, it would not be possible for a minute hand to point to 5. On the other hand, the old man admitted, there are a few ambiguous positions that might be interpreted in two different ways. The question is: how many times - during a 12 hour period- are the hands in such an ambiguous position?