bonanova Posted August 14, 2009 Report Share Posted August 14, 2009 A standard puzzle asks how many times between midnight and noon [not counting either] do the hour, minute and second hands of a clock point in the same direction? The result is not surprising that it never happens - 11 and 59 having no common factors. So let's ask instead: at what time(s) during the same interval are the three hands closest? . By closest we mean the smallest angle between the two hands farthest apart.We exclude the trivial answer that names a time very near noon or midnight. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 14, 2009 Report Share Posted August 14, 2009 (edited) A standard puzzle asks how many times between midnight and noon [not counting either] do the hour, minute and second hands of a clock point in the same direction? The result is not surprising that it never happens - 11 and 59 having no common factors. So let's ask instead: at what time(s) during the same interval are the three hands closest? . By closest we mean the smallest angle between the two hands farthest apart.We exclude the trivial answer that names a time very near noon or midnight. Without doing any arithmetic, I would say there are two answers, 1:05:05 and 11:54:54. Edited August 14, 2009 by jerbil Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 14, 2009 Report Share Posted August 14, 2009 No, 1:05:05 and 11:54:55. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 15, 2009 Report Share Posted August 15, 2009 I now have a detailed analysis of this problem for you, Bonanova. The principles are obvious, but the elementary arithmetic is fiddly, so I am going to check my calculations after I have had a rest before transmitting my detailed results, which I consider to be some time after 3 am and also some time before 9 am. Needless to say, my original guesses were totally wrong! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 15, 2009 Report Share Posted August 15, 2009 I append my detailed solution. I regret that no-one else found this problem intriguing. Clock Hands.doc Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted August 16, 2009 Author Report Share Posted August 16, 2009 I append my detailed solution. I regret that no-one else found this problem intriguing. Clock Hands.doc Nicely done! Bestowing the quasi-coveted bonanova Gold star award. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 18, 2009 Report Share Posted August 18, 2009 I append my detailed solution. I regret that no-one else found this problem intriguing. Clock Hands.doc au contraire....I just ran out of time to do this one at the same time as the other puzzles ... Quote Link to comment Share on other sites More sharing options...
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bonanova
A standard puzzle asks how many times between midnight and noon [not counting either]
do the hour, minute and second hands of a clock point in the same direction?
The result is not surprising that it never happens - 11 and 59 having no common factors.
So let's ask instead: at what time(s) during the same interval are the three hands closest?
.
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