Double-Pair-Hand Clock Problem
The red hands read 5:00, whereas there is no valid time representation for the blue hands.
As shown above, two colored poles are positioned on the analog clock, such that the pair of red hands always represents the correct time. At the same time, two poles rotate continuously with respect to the red hands.
Must two poles completely overlap for both pairs of different-colored hands to tell times correctly?
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1 solution
To answer the question, you can just imagine the scenario of the hands starting at 1 and then imagine how the opposite hands will work. You have a slow moving minute hand and a fast moving hour hand at 6 moving anticlockwise. It is clear that as the hour hand will move fast, it will reach a point that it will be in a valid time position before it even reaches 7 oclock.