A clock problem by Nihar and Julian (Part 2)
Take a 24 - hours digital clock. Now you must be bored seeing the same clock timings everyday. So now you keep that digital clock inverted upside-down. How many timings in the original clock are there such that they appear as "sensible numbers" when the clock is kept inverted upside-down?
Details And assumptions:
As an explicit example , if the timing shown in regular clock is \(06:19\) , then it will be seen as \(61:90\) in the inverted upside down clock and is one of our required timings . So you have to find the number of such timings.
If the timing is \(03:16\), upside down it would be \(91:E0\), and would not be accepted.
Note that after every \(23:59\), the clock shows \(00:00\) and not \(24:00\).
All digits look like this: (for clarifying the shape of digits)