Clock & Calendar

A clock has two main hands: Hour hand and Minute hand.
1. Minute Hand: Moves 6° in 1 minute (360°/60 min).
2. Hour Hand: Moves 0.5° in 1 minute (30°/60 min).
3. Relative Speed: Minute hand gains 5.5° per minute over the hour hand.

The angle (θ) between the hour hand and minute hand at H hours and M minutes is given by:
|30H - 5.5M| or θ = |30H - 112M|.

To find the mirror image time, subtract the given time from 11:60 (for 12-hour format) or 23:60 (for 24-hour format).

Odd days are the remaining days after dividing the total number of days by 7.
1. Ordinary Year: 365 days = 52 weeks + 1 Odd Day.
2. Leap Year: 366 days = 52 weeks + 2 Odd Days.
3. Century Leap Year: A century year is a leap year only if it is divisible by 400 (e.g., 2000 is a leap year, 1900 is not).