The backlit clock face in the town hall can be seen 24/7. The large blue hour hand is transparent, as is the larger red minute hand. When the minute hand passes over the hour hand, which happens about once every hour, there is a sudden very bright flash of purple. Nobody knows why the flash is so bright. How many such purple flashes will occur between 6:00 a.m. and 6:00 p.m.?
Solution
The hands will overlap eleven times. The overlaps occur at around 6:33 a.m., 7:38 a.m., 8:44 a.m., 9:49 a.m., 10:55 a.m., 12:00 p.m., 1:05 p.m., 2:11 p.m., 3:16 p.m., 4:21 p.m., and 5:27 p.m.