- Odd Days:
In any year, there are 52 complete weeks.
In a given period, the number of days more than the complete weeks are called odd days.
- Leap Year:
For a year to be a leap year,
- It should be divisible by 4.
- If it is divisible by 100, it should also be divisible by 400.
Note: A leap year has 366 days.
Examples:
- The years 884, 1564, 1600, 2000, 2012 are leap years.
- The years 431, 777, 1722, 2001, 2007, 2200 are not leap years.
- Ordinary Year:
The year, which is not a leap year, is called an ordinary year or a non-leap year.
An ordinary year has 365 days.
Examples:
- The years 573, 998, 2009 are ordinary years.
- The years 1700, 1800, 1900, 2100 are ordinary years.
- Counting of Odd Days:
First thing to remember is that the, 1^{st} January of the year AD 1 was a Monday and therefore, we must set Sunday as the 0^{th} day, Monday as the 1^{st} day,…, Saturday as the 6^{th} day.
Day of the week related to Odd days:
No. of odd days: | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
Day: | Sun. | Mon. | Tues. | Wed. | Thurs. | Fri. | Sat. |
Month of a year related to Odd days:
Month | Jan | Feb | Mar | April | May | June | July | Aug | Sep | Oct | Nov | Dec |
Days | 31 | 28/29 | 31 | 30 | 31 | 30 | 31 | 31 | 30 | 31 | 30 | 31 |
Odd days | 3 | 0/1 | 3 | 2 | 3 | 2 | 3 | 3 | 2 | 3 | 2 | 3 |
That is, 3 odd days for every month with 31 days, 2 odd days for every month with 30 days and 0/1 odd days for February.
Therefore, 1 ordinary year has 1 odd day.
Therefore, 1 leap year has 2 odd days.
(Why not 25 leap years? Because the 100^{th} year is a non-leap year.)
Tricks and shortcuts for quick calculation
- For making calculations quicker, the number of days/odd days in a year is given by
Months | Ordinary year | Leap year | ||
Days | Odd days | Days | Odd days | |
January 1 to March 31
April 1 to June 30 July 1 to September 30 October 1 to December 31 |
90
91 92 92 |
6
0 1 1 |
91
91 92 92 |
0
0 1 1 |
For example
To get the number of odd days of November 17^{th} of a particular year:
Odd days from January 1 to September odd days.
Odd days from October 1 to October 31 = 3 odd days.
Odd days from November 1 to November odd days.
Thus, total odd days of November 17^{th} odd days.
- Number of odd days of 1900 years = 1 odd day. Memorizing this is useful, as in most of the questions the year will be some year after 1900.
- The last day of a century must be Sunday, Monday, Wednesday or Friday. (The reason is given in Illustration 4.)
- An ordinary year always begins and ends on the same day of the week.
- For an ordinary year, February has exactly 4 weeks, so February and March always consecutively start on the same day of the week.
- Any date in March is the same day of the week as the corresponding date in November of that year. Another pair showing similar corresponding feature is April-July.
Conditions for calendars of two different years to be same
- Both the years must be of the same type. That is, either both must be non-leap years or both must be leap years.
- The net number of odd days for the period between these two years should be zero. That is, 1^{st} January of both the years must fall on the same day of the week.
“For detailed theory, refer the book “CSIR-NET General Aptitude – A New Outlook”