Calendar Problem

  1. 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.

  1. Leap Year:

For a year to be a leap year,

  1. It should be divisible by 4.
  2. 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.
  1. 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.
  1. Counting of Odd Days:

First thing to remember is that the, 1st January of the year AD 1 was a Monday and therefore, we must set Sunday as the 0th day, Monday as the 1st day,…, Saturday as the 6th 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 100th 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 17th 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 17th  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

  1. Both the years must be of the same type. That is, either both must be non-leap years or both must be leap years.
  2. The net number of odd days for the period between these two years should be zero. That is, 1st 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”

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