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 The hands of a clock (Posted on 2002-05-23)
Anne and Mike have an argument about the hands of the clock:

Anne: "The minute hand takes one hour to make a complete circle. Therefore, it will pass the hour hand once every hour!"

Mike: "But by the time the minute hand has made a full circle, the hour hand will have moved 1/12th of the circle ahead. And by the time the minute hand gets to that spot, the hour hand will have moved forward yet again. This will continue indefinitely, so it is obvious that contrary to what it may seem like, the minute hand will never pass the hour hand."

In reality, how often does the minute hand pass the hour hand?

 Submitted by levik Rating: 3.3636 (11 votes) Solution: (Hide) The hour hand takes 12 hours to make a full revolution around the face of the clock. The minute hand will have made 12 revolutions in that period of time, so it must have overtaken the hour hand (12 - 1 = 11) times. Since the hands are moving at a constant rate, each period between the clock hands' meeting is equal, and therefore they take place 12 hours / 11 times = 12/11th of an hour apart. (This is roughly 66 minutes, but you can calculate it exactly if you wish.)

 Subject Author Date Puzzle Solution: Method II K Sengupta 2008-05-19 05:48:10 Puzzle Solution: Method I K Sengupta 2008-05-19 05:47:04 Answer K Sengupta 2008-03-15 04:01:57 8th Grade ISAT Tim Campbell 2005-12-27 04:48:58 No Subject Steven Lu 2004-12-06 01:29:04 Achilles and the Tortoise !!!!!!!!! Penny 2003-12-17 02:58:17 re: solution Popstar Dave 2003-09-08 09:42:35 solution FatBoy 2003-09-03 10:19:19 And in more detail... Jim C 2003-06-05 09:33:32 quite easy really.... Matthew Bobbins 2002-12-15 10:18:18 Hmm... Gautam Joshi 2002-12-04 01:14:34 re: my solution Hope 2002-08-18 17:00:17 my solution shaun 2002-06-12 02:39:26 Simple counting. TomM 2002-05-23 13:29:24 Solution Ender 2002-05-23 04:27:41

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