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Wrist Watch


TimeSpaceLightForce
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A strange wrist watch have it hands separated equally on 9:05:25 am..and seem to be working properly.

The second hand runs at 1 rev per minute , the minute hand runs at 1 rev per hour while the hour hand runs 2 rev per day.

But everytime the hands overlaps they switch rotational speed.. Can you tell the rotational speeds of each hands when its

11:11:11 pm?

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@bonanova- yes they act like ordinary watches, you can tell the real time by knowing the
fastest and slowest hands.
@HMG -Good point! and welcome here..
it is mechanical and automatic..the hands turn a certain angle every seconds.
So it is still 11:11:11 until its 11:11:12 when all of the hands have moved.
Clue: Is 9:05:25 am same as 9:05:25 pm?
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A strange wrist watch have it hands separated equally on 9:05:25 am..and seem to be working properly.

The second hand runs at 1 rev per minute , the minute hand runs at 1 rev per hour while the hour hand runs 2 rev per day.

But everytime the hands overlaps they switch rotational speed.. Can you tell the rotational speeds of each hands when its

11:11:11 pm?

Does "when its 11:11:11 pm" refer to the actual time, or to the position of the hands?

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A strange wrist watch have it hands separated equally on 9:05:25 am..and seem to be working properly.

The second hand runs at 1 rev per minute , the minute hand runs at 1 rev per hour while the hour hand runs 2 rev per day.

But everytime the hands overlaps they switch rotational speed.. Can you tell the rotational speeds of each hands when its

11:11:11 pm?

Does "when its 11:11:11 pm" refer to the actual time, or to the position of the hands?

PM as in real time because when its 11:11:11 pm actual time, the 3 hands must be on "specific" angles..It can not be 2:56:11 or 11:11:10 or 2:10:56 actual time.
The hands' positions on 9:05:25am is same as 9:05:25pm (actual time) so the are actually around 2hrs,6min to figure this out..
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At 9:05:25 a regular wrist watch hands are at:

hr @ -87.291667 degrees

min @ 32.5 degrees

sec @ 150 degrees

therefore, a regular wristwatch cannot have its hands separated equally at 9:05:25. Hence, if a wristwatch has it hands separated equally at 9:05:25, it cannot be working properly. The question doesnt seem to be correct in stating BOTH "A strange wrist watch have it hands separated equally on 9:05:25 am." AND ".and seem to be working properly."

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At 9:05:25 a regular wrist watch hands are at:

hr @ -87.291667 degrees

min @ 32.5 degrees

sec @ 150 degrees

therefore, a regular wristwatch cannot have its hands separated equally at 9:05:25. Hence, if a wristwatch has it hands separated equally at 9:05:25, it cannot be working properly. The question doesnt seem to be correct in stating BOTH "A strange wrist watch have it hands separated equally on 9:05:25 am." AND ".and seem to be working properly."

Good point! The solution for The Complex Clock Puzzle (Equal Separation of Hands) should not affect this one.
..the hands turn a certain angle every seconds. So it is still 9:05:25 until all of the hands have moved to a certain equality of angles..before 9:02:26 where the watch still seem
(just looks like) to be working properly because the hands runs with proper speeds.
note: There is a pattern here ....
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Suppose the hr, min and sec hands behave like that of a normal watch at 00:00:00. Then, at 00:00:01 the sec hand is after the min hand which is after the hr hand. Note, that the hands remain in this configuration (i.e. h-m-s, hour hand before minute and minute before second hand in clockwise direction) but keep changing their speeds.

e.g. at 00:01:02 the configuration becomes (s-h-m) i.e. second hand is at hour's position, hr hand is at minute's

At 00:02:03 it becomes (m-s-h) i.e. minute hand is at hour's position and second hand is at minute's position

At 00:03:04 it returns to normal i.e. (h-m-s).

Note that all three configuration's above remain in this configuration (i.e. h-m-s, hour hand before minute and minute before second hand in clockwise direction) but keep changing their speeds. From the above 3 examples, Its clear that the hour hand position is taken up by second hand, then minute hand and then hour hand every time the second hand of a normal watch catches up with the hr hand of a normal watch i.e. after every 720/719 minutes. Similarly, the minute hand position is taken up by hr hand, then second hand and then minute hand, every time the second hand of a normal watch catches up with the minute hand of a normal watch i.e. after every 60/59 minutes. BUT, the configuration remains same, i.e. (h-m-s) in clockwise direction

UNTIL the hour hand and the minute hand get to swap their positions (i.e. every 720/11 minutes).

Thus, the clockwise order of hands, alternates between (h-m-s) and (m-h-s) every 720/11 minutes

The above example demonstrated that:

the clockwise order of hands, alternates between (h-m-s) and (m-h-s) every 720/11 minutes. Hence after 12 hours, the configuration reverses

the hour hand position is taken up by sec hand, then minute hand and then hr hand after every 720/719 mintes in h-m-s configuration

the minute hand position is taken up by hour, then second and then minute hand after every 60/59 minutes in h-m-s configuration

At 9:05:25 am the configuration is h-m-s. The difference between 9:05:25 am and 11:11:11 pm is 845.7667 minutes

Dividing this by 720/11 we get quotient as 12 which implies that the configuration remains as h-m-s

Dividing this by 720/719 we get quotient as 844 = 1 mod 3, hence hr position is occupied by second hand (OR second hand is moving the slowest)

Dividing this by 60/59 we get quotient as 831 = 0 mod 3, hence minute position is occupied by minute hand (OR minute hand is moving normally)

And second position is occupied by hr hand (OR hr hand is moving fastest)

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@ 9:06 it is H hand on 12 and fastest

@ 9:07 it is S hand on 12 and fastest

@ 9:08 it is M hand on 12 and fastest

@ 9:09 it is H hand on 12 and fastest

@ 9:10 it is S hand on 12 and fastest

@ 9:11 it is M hand on 12 and fastest

...

...so on

until it is 11:11:00 the fastest hand is on 12

should become minute speed at 11:11:11

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