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# Wrist Watch

## Question

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?

Edited by TimeSpaceLightForce

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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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The rotation speeds change between any overlapping pair or when all three overlap?

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The rotation speeds change between any overlapping pair or when all three overlap?

Exchange is between any overlapping pair. When all three overlaps they also exchange rotational speed but not in random order.

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But they always move forward?

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At 11:11:11 PM, they are all standstill and not moving.

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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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@ 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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