PROGRAMMING CHALLENGE 02/23 - CLOCK WISE
If by 0.4 seconds fuzz factor you mean the angle swept by 0.4 seconds on the clock, that's 2.4° or 2°24' or 0.0491 radians. With that as fuzz factor, it may be possible to achieve what you're looking for.
If you really meant your 0.4 seconds as equivalent to 2e-6 radians, that [more precisely 1.94e-6] is equal to 0.4 arc-seconds -- 0°0'0.4" -- in which case it's not possible to get coincidence of all three hands within that fuzz factor.
The first occurrence of the hour and minute hands coinciding is when the hour hand has gone 1/11 of all the way around, which is at 5.4545... minutes past 1:00. That's 5 minutes and 27.2727... seconds, so the second hand aims in quite a different direction than the other two. Back that off until the second hand hits where the other two were when they coincided, and the minute hand will back off by 2.1822727...°, far outside the 0.4 arc-seconds tolerance. But not quite outside a tolerance of 0.4 clock-seconds.
@CodeDing wrote:
.... Here are the 11 overlap times .....
Those are the overlap times of the hour hand and the minute hand. The second hand doesn't coincide with those two at any of those times, though at two of them it's only about 5 seconds away, so when it coincides with one of them, all three could be within the fuzz factor of each other.
We may have a winner, look carefully at the image for the Author name ! Another great one by him.
Current time day etc.
Purely mathematical solution for "ideal mechanical clock":
(defun c:timeoverlaps (/ test_hours )
(defun to_hms (secs / hrs rem1 mins rem2 secs test_hours delseconds i overlaps)
(setq
hrs (/ secs 3600.0)
rem1 (rem secs 3600.0)
mins (/ rem1 60.0)
rem2 (rem mins 1.0)
secs (* rem2 60.0)
)
(strcat (rtos hrs 2 0) ":" (rtos mins 2 0) ":" (rtos secs 2 2))
)
(setq test_hours 12 delseconds (+ (* 65 60) (* (/ 5.0 11) 60)) i -1 )
(while (< (setq i (1+ i)) test_hours)(setq overlaps (cons (* i delseconds) overlaps)))
(mapcar 'princ (mapcar '(lambda (x)(strcat "\n" x)) (mapcar 'to_hms (reverse overlaps))))
(princ)
)1:5:27.27
2:11:54.55
3:16:21.82
4:22:49.09
5:27:16.36
7:33:43.64
8:38:10.91
9:44:38.18
10:49:5.45
11:55:32.73
12:0:0
If we look at this clock hands overlaps we can see that seconds are actually wrong for every but last result.
Since we know that seconds hand is 60 times faster than minutes hand and 720 times faster than hours hand, seconds are irrelevant to final solution since at overlap times all three hand will stay on a mechanical watch within assumed angular tolerance. So correct clock hands overlap times are:
(defun c:timeoverlaps2 (/ test_hours )
(defun to_hms (secs / hrs rem1 mins rem2 secs test_hours delseconds i overlaps)
(setq
hrs (/ secs 3600.0)
rem1 (rem secs 3600.0)
mins (/ rem1 60.0)
rem2 (rem mins 1.0)
secs (* rem2 60.0)
)
(strcat (rtos hrs 2 0) ":" (rtos mins 2 0) ":" (rtos mins 2 0))
)
(setq test_hours 12 delseconds (+ (* 65 60) (* (/ 5.0 11) 60)) i -1 )
(while (< (setq i (1+ i)) test_hours)(setq overlaps (cons (* i delseconds) overlaps)))
(mapcar 'princ (mapcar '(lambda (x)(strcat "\n" x)) (mapcar 'to_hms (reverse overlaps))))
(princ)
)1:5:5
2:11:11
3:16:16
4:22:22
5:27:27
7:33:33
8:38:38
9:44:44
10:49:49
11:55:55
12:0:0
Miljenko Hatlak
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Those can't all be correct, for example, there can't be one between 11:00 and 12:00 just as there can't be one between 12:00 and 1:00, and there has to be one [hour-&-minute-hands, at least] between 6:00 and 7:00. But even for those that agree with Message 7, they have the same problem described in Message 8.
@Kent1Cooper Check my edited post above
Miljenko Hatlak
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Something is still not right. Surely they won't coincide at 11:55:55. The last one before 12:00 would have to be exactly as far before 12:00 as the first one is after it.
