A clock problem by Nihar and Julian (Part 1)

Logic Level 3

Take a 12 - 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?

Let $$S$$ be the number of such timings. Input your answer as $$S+28$$.

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 $$11:59$$, the clock shows $$00:00$$ and not $$12:00$$.

• All digits look like this: (for clarifying the shape of digits)

×