## Clocks/Calendars

A digital clock at Ghanta Ghar, Chandni Chowk shows time in MM : DD : HH : mm : SS format, where DD stands for the date of the month, MM stands for the month, HH stands for hours, mm is for minutes and SS is for seconds. The HH in the clock is in 24 hours format, so it can be maximum 23.
For example, if it is 29 July and the time of the day is 9:40:04 p.m., then that clock will show 07 : 29 : 21 : 40 : 04.

One day, while looking at the clock, Nishikant noticed that all the digits in the time shown by the clock are distinct.

1. If the time, when Nishikant noticed, is the earliest possible of the year using all distinct digits, then what must be the digits at the place of HH?

2. If the time, when Nishikant noticed, is maximum possible of the year using all distinct digits, then what must be the value of SS?

3. What can be the maximum number of 4’s in this clock at any time, if all the digits in the clock are not necessarily distinct?

4. How many distinct times are possible with all distinct digits?