Calendar - Important Formulae

1. Odd Days:
   We are supposed to find the day of the week on a given date.
   For this, we use the concept of 'odd days'.
   In a given period, the number of days more than the complete weeks are called odd days.
2. Leap Year:
   (i). Every year divisible by 4 is a leap year, if it is not a century.
   (ii). Every 4^th century is a leap year and no other century is a leap year.
   Note: A leap year has 366 days.
   Examples:
   1. Each of the years 1948, 2004, 1676 etc. is a leap year.
   2. Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.
   3. None of the years 2001, 2002, 2003, 2005, 1800, 2100 is a leap year.
3. Ordinary Year:
   The year which is not a leap year is called an ordinary years. An ordinary year has 365 days.
4. Counting of Odd Days:
   1. 1 ordinary year = 365 days = (52 weeks + 1 day.)
       1 ordinary year has 1 odd day.
   2. 1 leap year = 366 days = (52 weeks + 2 days)
       1 leap year has 2 odd days.
   3. 100 years = 76 ordinary years + 24 leap years
        = (76 x 1 + 24 x 2) odd days = 124 odd days.
        = (17 weeks + days)  5 odd days.
       Number of odd days in 100 years = 5.
      Number of odd days in 200 years = (5 x 2)  3 odd days.
      Number of odd days in 300 years = (5 x 3)  1 odd day.
      Number of odd days in 400 years = (5 x 4 + 1)  0 odd day.
      Similarly, each one of 800 years, 1200 years, 1600 years, 2000 years etc. has 0 odd days.
5. Day of the Week Related to Odd Days:

   No. of days:	0	1	2	3	4	5	6
   Day:	Sun.	Mon.	Tues.	Wed.	Thurs.	Fri.	Sat.

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