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What time is it again? (Posted on 2005-06-19) Difficulty: 1 of 5
What time is it if the second hand is exactly on a second mark, and exactly 18 second marks ahead of the hour hand?

See The Solution Submitted by Erik O.    
Rating: 3.0000 (3 votes)

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Solution trial and (no) error - computer solution | Comment 1 of 8

"no error" because the first trial, with the second hand straight up, gives the correct answer: 8:24.

There are 60 possible positions for the second hand, 0 through 59 seconds past the latest minute. By the conditions of the problem, this places the hour hand on a particular positon 18/60 of a circle back on the clockface (or 42/60 ahead, so as not to consider negative positions).  The number of hours past 12 (or zero) is the second (aka minute) position of the hour hand divided by 5, so the time in seconds would be the position of the hour hand divided by 5 and multiplied by 3600 for the number of seconds in an hour.

If that time of day, now converted to seconds is in fact the seconds position assumed, the given time is the answer.

As it happens, this occurs when the second hand is actually straight up, zero seconds past the integral minute.  The hour hand is then at the 42 mark for minutes or seconds, 18 units before the second hand.

DEFLNG A-Z
CLS
FOR i = 0 TO 59
 t = i
 t2 = t MOD 60
 t2 = t2 - 18: IF t2 < 0 THEN t2 = t2 + 60 ' seconds pos of hr hand
 t2 = t2 * (3600 / 5)
 ts = t2 ' time in seconds
 t2 = t2 MOD 60
 IF t = t2 THEN
   h = ts \ 3600: ts = ts - h * 3600
   m = ts \ 60: ts = ts - m * 60
   PRINT h; ":"; m; ":"; ts, t, t - t2
 END IF
NEXT

If the IF ... END IF were removed, you'd get

 Time        sec hand at   discr. diff from 18 
 8 : 24 : 0    0             0
 8 : 36 : 0    1             1
 8 : 48 : 0    2             2
 9 : 0 : 0     3             3
 9 : 12 : 0    4             4
 9 : 24 : 0    5             5
 9 : 36 : 0    6             6
 9 : 48 : 0    7             7
 10 : 0 : 0    8             8
 10 : 12 : 0   9             9
 10 : 24 : 0   10            10
 10 : 36 : 0   11            11
 10 : 48 : 0   12            12
 11 : 0 : 0    13            13
 11 : 12 : 0   14            14
 11 : 24 : 0   15            15
 11 : 36 : 0   16            16
 11 : 48 : 0   17            17
 0 : 0 : 0     18            18
 0 : 12 : 0    19            19
 0 : 24 : 0    20            20
 0 : 36 : 0    21            21
 0 : 48 : 0    22            22
 1 : 0 : 0     23            23
 1 : 12 : 0    24            24
 1 : 24 : 0    25            25
 1 : 36 : 0    26            26
 1 : 48 : 0    27            27
 2 : 0 : 0     28            28
 2 : 12 : 0    29            29
 2 : 24 : 0    30            30
 2 : 36 : 0    31            31
 2 : 48 : 0    32            32
 3 : 0 : 0     33            33
 3 : 12 : 0    34            34
 3 : 24 : 0    35            35
 3 : 36 : 0    36            36
 3 : 48 : 0    37            37
 4 : 0 : 0     38            38
 4 : 12 : 0    39            39
 4 : 24 : 0    40            40
 4 : 36 : 0    41            41
 4 : 48 : 0    42            42
 5 : 0 : 0     43            43
 5 : 12 : 0    44            44
 5 : 24 : 0    45            45
 5 : 36 : 0    46            46
 5 : 48 : 0    47            47
 6 : 0 : 0     48            48
 6 : 12 : 0    49            49
 6 : 24 : 0    50            50
 6 : 36 : 0    51            51
 6 : 48 : 0    52            52
 7 : 0 : 0     53            53
 7 : 12 : 0    54            54
 7 : 24 : 0    55            55
 7 : 36 : 0    56            56
 7 : 48 : 0    57            57
 8 : 0 : 0     58            58
 8 : 12 : 0    59            59
 8 : 24 : 0    60            60

  Posted by Charlie on 2005-06-19 15:36:59
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