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The right time (Posted on 2019-05-02) Difficulty: 2 of 5
During each hour, the clock hands will always make a right angle twice.

Will the time gap between these 2 instances be constant for every hour?

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution solution Comment 1 of 1
The hour hand goes at 30° per hour.
The minute hand goes 360° per hour.

The minute hand goes 330° per hour relative to the hour hand; it needs to travel 180° relative to the hour hand to get from making a 90° angle on one side to a 90° angle on the other side, taking 180/330 of an hour, or 6/11 of an hour, regardless of which hour.

Of course the hand makes one fewer than 12 revolutions relative to the other hand in 12 hours as it takes 12/11 as much time to make one complete revolution to the same 90° advance spot. This still enables the first statement to be true as 3 o'clock and 9 o'clock have occasions shared between two hours, each sharing only one such right angle position--leading or trailing.

So the answer is yes; there can't be variable length intervals.

  Posted by Charlie on 2019-05-06 11:33:25
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