Best Answer m00li, 12 May 2014 - 02:30 AM

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)**