IBM Ponder This #133 · May 2009

Find all times that when viewed as

1. an analog watch, the second hand is a bisector of the angle between the minute hand and the hour hand.
2. a digital watch, the time is palindrome.

Update (05/01): To clarify: the time should satisfy both conditions when the analog clock moves continuously, while the digital one is rounded to the nearest second and shows the time in hh:mm:ss format.

Solution

Best opened after a real attempt

To be added.