Calender

Some Definitions:-
Odd Days : The number of days more than complete number of weeks in a given period are called odd days. In other words , In a given period, the quantity of days more than the complete weeks are called Odd days or the remainder obtained when the given number of days is converted into weeks by dividing by 7.
Example : The number of odd days in a period of 57 days is => 1.

Note => 7a + b odd days , where b is less than or equal to is equivalent to number of odd days .
27 odd days= 7 x 3 + 6 = 6 odd days

Leap Year: Every year divisible by 4 in a leap year. But not all century years are leap years. Only those century years which are divisible by 400 are leap years and other century years are ordinary years. As an example, 1100, 1300, 1400, 1500, 1700 are ordinary years but 1200, 1600, 2000
are leap years. So every 4th century is a leap year.

Ordinary Year: A non-leap year is an ordinary year. A conventional year has 365 days. A leap year has 366 days.

Method Of Counting Odd Days:-
For An Ordinary Year:- It has 365 days (52 weeks+ 1 day)
?
It has 1 odd day.
For A Leap Year:-
It has 366 days = (52 weeks+2 days)
?
It has 2 odd days.

For A Period Of 100 Years:- 100 year =76 normal year +24 leap year
= (76x1+24x2) odd days =124 odd days
= (17 weeks +5 days) =5 odd days.

For A Period Of 200 Years:-
= 3

For A Period Of 300 Years:-
(5x3) =1 odd day.

For A Period Of 400 Years:-
(5x4+1) = 0 odd days.

EACH MULTIPLE OF 400 i.e. 800 years, 1200 years, 1600 years, 2000 years and so on has 0 odd days.
Corresponding days on ODD days.

No. of odd days: - Days:
0 - Sun
1 - Mon
2 - Tue
3 - Wed
4 - Thu
5 - Fri
6 - Sat

Some Points To Keep In Mind:-
1. February: 28 days(ordinary year) gives '0' odd days, 29 days (leap year) gives '1' odd day.
2. January, March, May, July, Aug, Oct and Dec have 31 days each and So give '3' odd days.
3. April, June, Sep and Nov each have 30 days and So give '2' odd days.
4. An ordinary year has 365 days. So we divide 365 by 7 to get the complete number of weeks and the e-remainder will be the odd days: as 365=(7×52)+1.
5. An ordinary year has 1 odd day .Since a leap year has 366 days, there will be 2 odd days.
6. The last day of a century cannot be a Thursday or a Saturday.
7. The first day of a century must be a Monday, a Tuesday, a Thursday or Saturday.