A METHOD TO FIND OUT THE WEEK DAY FOR ANY DATE

A METHOD TO FIND OUT THE WEEK DAY FOR ANY DATE


1 week = 7 days
1 year = 365 days
If we divide 365 by 7
We get 7) 365 (52
                 35
                ____
                 15
                 14
               _____
                   1
               _____
So, when we divide 365 days (=1 year) by 7 we get a remainder 1
For 1 year the reminder is 1
For 100 years the remainder will be (100 *1) = 100
In 100 years the No of Leap year                    =   24
                                                                            ___
                                                                            124
                                                                            ___
If we divide 124 by 7, we get a remainder 5

           7) 124 (17
                 7
               ____
                 54
                 49
              _____
                   5
              _____

For 1 year the reminder = 1
For 100 years the remainder = 5
For 400 years the remainder = (4*5) = 20
(400th year is leap year, hence add 1)     1
                                                             ___
                                                              21
                                                             ___
(100th, 200th and 300th years are not leap years, whereas 400th year is leap year)

If we divide 21 by 7 we get a remainder 0

7) 21(3
    21
--------
      0
-------

If we summarize the above,

For 1 year the reminder = 1
For 100 years the remainder = 5
For 400 years the remainder = 0

Example1

28-07- 1968

To find out a week day for the given year, we have to calculate remainder for the year previous to the given year.

Here the given year is 1968, so we have to find out the remainder for the year 1967

We can write the year 1967 as below
The remainders we get when divide by 7

 (4*400) =                                1600 = 4*0   = 00 = 00
 (3*100) =                                  300 = (3*5) =15 = 01 (15/7= Quotient =2, Remainder =1)
 (67*1)   =                                    67 =                      04 (67/7=Quotient =9, Remainder =4)     
 In 67 years the No leap years = 16 =                       02(16/7= Quotient =2, Remainder =2)
                                                                                 ------
                                                                                   07
                                                                                 ------

Remainder for the year 1967 = 07
Jan 1968                                 = 31
Feb 1968                                = 29 (Year 1968 is a leap year)
Mar 1968                                = 31
Apr 1968                                = 30
May 1968                               = 31
Jun 1968                                 = 30
July 1968                                = 28
                                                -----
                                                217
                                                -----

7)217(31
   217
-------
      0
--------
If the remainder is 0 the day is Sunday
If the remainder is 1 the day is Monday
If the remainder is 2 the day is Tuesday
If the remainder is 3 the day is Wednesday
If the remainder is 4 the day is Thursday
If the remainder is 5 the day is Friday
If the remainder is 6 the day is Saturday

28-07-1968 is Sunday


Example 2

02-12-2011

Here the given year is 2011, so we have to find out the remainder for the year 2010

We can write the year 2010 as below
The remainders we get when divide by 7

(4*400)= 2000= 4*0                    = 00
(10*1)  =     10                              = 03 (10/7=Quotient =1, Remainder =3)  
 In 10 years the No. of leap years = 02
                                                        -----
                                                         05
                                                        -----


Remainder for the year 2010= 05
Jan 2011                                = 31
Feb 2011                               = 28 (Year 2011 is not a leap year)
Mar 2011                               = 31
Apr 2011                               = 30
May 2011                              = 31
Jun 2011                                = 30
July 2011                               = 31
Aug 2011                               = 31
Sept 2011                              = 30
Oct 2011                                = 31
Nov 2011                               = 30
Dec 2011                                = 02
                                                -----
                                                341
                                                -----



7)341(48
   28
-------
     61
     56
-------
     05
-------
Remainder 05 = Friday