IMPORTANT FORMULA FOR CALENDER BASED PROBLEMS

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.