Calendar
We know thatBefore we proceed ahead, we should be very clear about two things:
Which years are leap years?
It takes the earth about 365.2422 days to go around the sun, but a normal calendar year is only 365 days. The extra fraction of a day added up four times makes four years (or, four revolution of earth around sun) 1460.9688 days, but four calendar years would only be 1460 days. That 0.9688 is almost a whole day, so every four years we add an extra day to our calendar, February 29. We call that year leap year. To make things easier, leap years are always divisible by four: 2004 and 2008 will both be leap years.
Rule 
Examples 
Every fourth year is a leap year. 
2004, 2008, and 2012 are leap years. 
However, every centenary year is not a leap year. 
1900 and 2100 arenot leap years. 
In case of centuries, every four hundred years, thereâ€™s a leap year after all. 
2000 and 2400 are leap years. 
In layman terms, all the century years divisible by 400 will be leap years and all the noncentury years divisible by 4 will be leap years. So, leap year next to 2096 AD is 2104 AD and not 2100 AD.
Because 2000, 4000, 6000, etc. are leap years and 1000, 3000, 5000, etc. are not, the number of leap days in each millennium alternates between 242 and 243, with the first, third, etc. millennia (i.e., 1â€“1000, 2001â€“3000, etc.) having 242 leap days, and the second, fourth, etc. (i.e., 1001â€“2000, 3001â€“4000, etc.) having 243 leap days.
How the days of consecutive years change?
Due to any nonleap year, calendar of next year go ahead by 1 day and due to any leap year, calendar of next year goes ahead by 2 days, but this change in calendar will be there only before 29th February.

1991 
1992 
1993 
1st January 
Sunday 
Monday 
Wednesday 
28th February 
Tuesday 
Wednesday 
Friday 
1st March 
Wednesday 
Friday 
Saturday 
In the above example, we have assumed that 1st January of 1991 is Sunday. 1991 and 1993 are nonleap years and 1992 is a leap year.
If now we try to find out the symmetricity of calendars, we can see this in the following way:
 For any leapyear
Year 
1972 
1973 
1974 
1975 
1976 
Excess days 
2 
1 
1 
1 
2 
Since no. of excess days are 7, so the days of the year 1972 and year 1977 will be same from 1st of January and 28th of February.
 For any (leapyear+1) year
Year 
1973 
1974 
1975 
1976 
1977 
1978 
Excess days 
1 
1 
1 
2 
1 
1 
Since no. of excess days are 7, so calendar of year 1973 and 1979 will be same for whole year.
 For any (leapyear + 2) year
Year 
1974 
1975 
1976 
1977 
1978 
1979 
Excess days 
1 
1 
2 
1 
1 
1 
Since excess days are 7, so calendar of year 1974 and 1980 will be same till 28th of February.
 For any (leapyear + 3) year
Year 
1975 
1976 
1977 
1978 
1979 
1980 
1981 
1982 
1983 
1984 
1985 
Excess days 
1 
2 
1 
1 
1 
2 
1 
1 
1 
2 
1 
Since no. of excess days are 14, so calendar of year 1975 and 1986 will be same for whole year.
This whole mechanism can be summed up in following way:
Nature of year 
No. of years after which 1st January will be same 
Leap year 
5 
Leap year + 1 
6 
Leap year + 2 
6 
Leap year + 3 
11 
So, if 1st January of 1972 and 1st January of 1977 will be on same day.
Exception
Finding day of a date by using a reference date
Let us see this with the help of an example: If 9th Dec of 1972 is Sunday, then which day it will be on 14th December 1998? Year Method â€“ We use the above given table to find out about any of the years.
 Days method â€“ We use the no. of excess days every year to find out the no. of days calendar will move ahead by.
 Actual Calculation method â€“ With the help of this method, we can find the actual day of any date of 20th century. To use this method effectively, we need to remember the Month Codes of all the months.

Jan 
Feb 
Mar 
Apr 
May 
Jun 
Jul 
Aug 
Sep 
Oct 
Nov 
Dec 
Leap Year 
0 
3 
4 
0 
2 
5 
0 
3 
6 
1 
4 
6 
Nonleap year 
1 
4 
4 
0 
2 
5 
0 
3 
6 
1 
4 
6 