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 On the clock (Posted on 2007-03-23)
How many times per day, and at what time(s) do the hour and minute hands on a clock form EXACTLY a 60 degree angle?

 See The Solution Submitted by Sing4TheDay Rating: 3.0000 (3 votes)

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 ... and at what times | Comment 2 of 7 |

The times the situation occurs come in pairs, equally before and after the two hands meet (0-degree separation). As the two hand meet 22 times a day, that situation happens every 65 5/11 minutes, starting at 12:00. The 60-degree situation happens 1/6 of this time interval, both before and after each 0-degree separation. That's 10 10/11 minutes before and after noon, and repeated every 65 5/11 after each preceding occurrence.

0:10  10/11
0:54  6/11
1:16  4/11
2:00
2:21  9/11
3:05  5/11
3:27  3/11
4:10  10/11
4:32  8/11
5:16  4/11
5:38  2/11
6:21  9/11
6:43  7/11
7:27  3/11
7:49  1/11
8:32  8/11
8:54  6/11
9:38  2/11
10:00
10:43  7/11
11:05  5/11
11:49  1/11
12:10  10/11
12:54  6/11
13:16  4/11
14:00
14:21  9/11
15:05  5/11
15:27  3/11
16:10  10/11
16:32  8/11
17:16  4/11
17:38  2/11
18:21  9/11
18:43  7/11
19:27  3/11
19:49  1/11
20:32  8/11
20:54  6/11
21:38  2/11
22:00
22:43  7/11
23:05  5/11
23:49  1/11

 Posted by Charlie on 2007-03-23 09:07:51

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