Calendars
If someone asks us what day it was on 10th April , 1924 or what
day it would be on 14th July 2475, we feel these are crazy questions. But if
you know the rule how to find it , it is very easier task.
The clue to the process of finding the day of the week on a
particular date lies in finding the number of odd days , which is
different from the odd numbers.
ODD DAYS : The number of days more than
complete number of weeks in a given period are called odd days.
In other words , 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 72 days is => 2.
Note => (7a +b) odd days , where b is less than or equal
to is equivalent to number of odd days .
17 odd days= 7 x 2 + 3 = 3 odd days
LEAP YEAR: A year which is
exactly divisible by 4 is leap year.
For example: 1984, 1624,2012, etc.
For a century year to be the leap year it must be divisible by
400. thus years 400, 1200, 1600, 2000 are leap years. And 500,1100,1300,1500
etc are not leap years ( because they are not exactly divisible by 400).
An ordinary year has 365 days. Therefore we divide 365 by 7 to get
the complete number of weeks and the remainder will be the odd days: as
365=(7×52)+1.
An ordinary year has 1 odd
day
.
Since a leap year has 366 days, there will be 2
odd days.
Things to be remembered:
100 years = 76 ordinary years + 24 leap years.
(Note that 100/4=25, but since 100^{th} year is not a
leap year as it is not visible by 400, we have only 24 leap year)
100 years= (76×1)+(24×2)
= 76+48 = 124 = (7×17)+5
Thus there will be 5 odd days, in 100 years.
In 200 years there will be > 2×5=10=(7×1)+3 =3 odd days.
In 300 years there will be > 3×5=15=(7×2)+1 =1 odd day
In 400 years there will be >4×5+1 leap year=21 = 7×3+0=0 odd
days.(Every 400^{th} year is a leap year. Therefore additional day
is added)
Therefore each one of 800, 1200, 1600, 2000 years will leave zero
(0) odd days.
To
summarize
Years

Number of odd
days

Example year

Number of odd
days

Ordinary

1

2009

1

Leap

2

2008

2

100

5

1700

5

200

3

1800

3

300

1

1900

1

400

0

2000

0

Symmetricity of Calendars (
Repetition of the calendar )
For a leap Year :
Let us see , for example , the case of 2004 .
Year 2004 2005 2006
2007 2008
Odd days 2
1 1
1 2
Since , the number of odd days are 7 , so days of the year
2004 and 2009 will be same from 1st January to 28 th February . (
Because 2009 is not a leap year )
To know which year will have the same calender as the given leap
year , add 28 to given leap year i.e 2004 +28 =2032 will have the
same calendar like 2004 for the whole year
For any ( leap year + 1) year :
Let us take an example , 2005
Year 2005 2006 2007 2008 2009 2010
Odd days 1 1 1 2 1 1
Since the number of odd days are 7 , so calendars of 2005 and 2011
will be same for whole year.
Any ( leap year +1) , the
same calendar will happen after 6 years . 2005 + 6 =2011
For any ( leap year + 2) year :
Let us take an example , 2006
Year 2006
2007 2008 2009 2010
2011
Odd days 1
1 2
1 1
1
Since the number of odd days are 7 , so calendars of 2006 and 2012
will be same till 28th February.
Any ( leap year + 2) , the
same calendar will happen after 6 years . 2006 + 6 =2012
For any ( leap year + 3) year :
Let us take an example , 2007
Year 2007
2008 2009 2010 2011 2012
Odd days 1
2 1
1 1 2
Year 2013 2014 2015 2016 2017
Odd Days 1 1 1 2 1
Year 2013 2014 2015 2016 2017
Odd Days 1 1 1 2 1
Since the number of odd days are 14 , so calendars of 2007 and
2018 will be same for whole year.
Any ( leap year +3) , the
same calendar will happen after 11 years .
2007 + 11 =2018
2007 + 11 =2018
Symmetricity of Calendars ( Months in a year)
The following data gives the
months in which the same calendar can be used, i.e, the corresponding dates of
the follow the same week day.
Leap Year: January & July,
February & August.
NonLeap Year: January & October,
February & March
Any year, leap or non leap year: March & November, April
& July, September & December
Important Note :
i) The
last day of a century cannot be a Thursday, Tuesday or a Saturday.
ii) The
first day of a century must be a Monday, a Tuesday, a Thursday or Saturday.
For more solved problems and examples, go through Problems on
Calendars
For TCS placement questions on calendars , visit TCS PLACEMENT QUESTIONS ON CALENDARS
For TCS placement questions on calendars , visit TCS PLACEMENT QUESTIONS ON CALENDARS