Time
Hour Hand in degrees.
Minute Hand in degrees.
Second Hand in degrees.
12:22:42
H 11
M 132
S 252
12:42:27
H 21
M 252
S 162
1:26:46
H 43
M 156
S 276
1:27:47
H 43.5
M 162
S 282
1:48:28
H 54
M 288
S 168
2:32:52
H 76
M 192
S 312
2:33:53
H 114.54
M 198
S 318
2:54:32
H 87
M 324
S 192
2:54:34
H 82.5
M 270
S 204
3:38:58
H 109
M 228
S 348
As long as the minute and seconds hands are 120 appart, the hour hand NEVER falls between them. Midnight is the only answer where it works. Prove me wrong, but it won't work.
😠😉
If the clock is completely analog then it never works. Each hour there are two times when the hour hand and minute hand are 120 degrees apart, these are (note seconds are show to 2decimal places)
00:21:49.09
00:43:38.18
01:27:16.36
01:49:05.45
02:32:43.64
02:54:32.73
03:38:10.91
04:00:00.00
Unfortunately at these exact time the second hand is not 120 degrees away from both.
If instead we deal with a discrete clock, ie one where the hands can only exist in one of the 60 positions, and assuming that the minute hand doesn't move until the second hand moves from 59 to 00 and the hour hand moves only as the minute hand moves each 12th time then the following times fullfill the criteria
00:21:41
00:43:23
01:27:47
01:49:29
02:12:31
02:43:23
03:17:37
03:59:39
Any questions? :-)
16h40. This has to be the answer because due to the innatly evil nature of the universe, and the fact that fate likes to have a laugh at our expense.
It would stop at a time that so that if I looked at it in the early afternoon I would be given that brief jolt of joy that I could go home soon until I remembered that the clock was broken & I really had 4 hours to go. Likewise it has to be close to 5pm but not quite so that if I glance at it when it really is past 5 I don't realise and work too long.
Forget maths, just remember that fate is out to get you.