CALENDER

              CALENDAR

Odd day :
The number of days in a given period in excess of a multiple of 7 is the number of odd days., e.g., in a year of 365 days there are 52 weeks (i e.,364 days) and balance is 1 odd day.

Ordinary year :
contains 365 days. i.e., 52 weeks and 1 odd day.

Leap year :
contains 366 days i.e., 52 weeks and 2 odd days. A year divisible by 4 is a leap year e.g., 1984, 1998, 1992 etc and not 1977, 1982 etc.
 In a case of century years, only those divisible by 400 are leap years e.g., 400, 800, 1200 etc. are leap years and not 100, 200, 500, 600, 700 etc, although they are divisible by 4.

Calculation odd days:
1) 100 years has 24 leap years (not 25) and 76 ordinary years.
= (24 x2)+ (76 x 1) odd days.
= 124 odd days.
= 17 weeks + 5 odd days (number of odd days are always in excess of weeks hence odd days <7).

2) 200 years has (5 x 2)=10 odd days
=  one week + 3 odd days.
So, 200 years has 3 odd days.

3) similarly 300 years has 1 odd day.

4) 400 year has (5 x 4 = 20 odd days + 1 odd day (every 400th year is a leap year)
=  21 odd days 
= 0 odd day

TO FIND THE DAY OF THE WEEK ON A PARTICULAR DATE WHEN NO REFERENCE DAY IS GIVEN.

Assumption: 1st January, 1 A. D, was a Monday.

Step 
1) count the number of odd days on the given date.
2) write Sunday for 0 odd day.
    write Monday for 1 odd day.
    Write Tuesday for 2 odd days.
    Write Saturday for 6 od days.
( 7 odd day means 0 odd day which is again Sunday)

Example: What day of the week was 3rd May 1999 ?

Solution:
3rd May 1999 means,
 1998 complete years + first 4 months up to April of 1999 + 3 days of May 1998 years.
= 1600 years (of zero odd days) 
+ 300 years (of 1 odd day) 
+ 98 years (24 leap years + 74 ordinary years) 
(of 122 odd days= 17 weeks + 3 odd days)
So, 1998 years have (0+1+3)= 4 odd days.
 January =31 days => 4 weeks + 3 odd days.
February '99= 28 days=> 0 odd days
 March= 31 days => 4 weeks + 3 odd days.
 April = 30 days => 4 weeks + 2 odd days.
May= 3 days => 3 odd days.
 Total= (4+3+0+3 +2+3)=15 odd days.
=  2 weeks + 1 odd day.
So, 3rd May 1999 was Monday.

 TO FIND DAY OF THE WEEK ON A PARTICULAR DATE WHEN  REFERENCE DAY IS GIVEN 

STEP
1) find the net number of all days for the period between reference date and the given date. (exclude reference date)

2) the day of the week on the particular date is equal number of net odd days ahead of reference day (if the reference day was before the date) but behind the reference day (If this date was behind the reference day).
 
Example January 16, 1997 was a Thursday. What day of the week will it be on January 4, 2000 ?

Solution:
 In between 1997, 1998, 1999 are not leap years.
  1998 and 1999 together have 2 odd days.
Number of days remaining 1997
=  365 +6 odd days.
 =349 days 
 Total number of odd days
= 2+ 6 + 4 = 12 days.
= 1 week + 5 odd days.
Since, January 16, 1997  is before January 4, 2000.
Hence it will be on Tuesday.


             PROBLEMS

1) 2 days before yesterday was Monday, then what day of the week will be day after tomorrow ?
a) Sunday b) Tuesday c) Thursday  d) Saturday 

2) if a day before yesterday was wednesday, then when will Sunday fall ?
a) 3rd day after today b) tomorrow c) today d) A day after tomorrow

3) If the 25th of August in a year is Thursday, the number of Monday's in that month is
a) 3 b) 4 c) 5  d) cannot be determined 

4) If February 1, 2008 is Wednesday , what day is March 3, 2008?
a) Sunday b) Saturday  c) Friday d) Monday

5) what was the day of the week on 26 January 2012 ?
a) Sunday b) Saturday c) Thursday d) Tuesday

6) what will be the day of the week on 15th August 2021 ?
a) Sunday b) Wednesday c) Saturday d) Monday 

7) what was the day of the week on the 26th January 1951 ?
a) Friday b) Saturday c) Sunday d) Monday 

8) what was the day of the week on 23rd November 1987 ?
a) Tuesday b) Monday c) Thursday d) Saturday

9) what was the day of the week on 14th January 1994?
a) Friday  b) Monday c) Sunday d) Tuesday 

10) if it was a Saturday on 10th November 2018, what was the day of the week on 15th August 2017?
a) Monday b) Tuesday c) Sunday  d) Friday

11) if it was a Sunday on1st January 2017, what was the day of the week on 31st December 2017 ?
a) Tuesday b) Monday  c) Sunday  d) Friday

12) if 27th March, 1995 was a Monday then what day of the week was 1 November, 1994 ?
a) Sunday b) Monday  c) Tuesday d) Wednesday 

13) what was the day on 2nd July, 1984
a)  Wednesday b) Tuesday  c) Monday d) Thursday

14) it is observed that January 1, 2023 is a Sunday. In which year again the January 1st will fall on a Sunday ?
a) 2029  b) 2030  c) 2034 d) 2037

15) The year next 1990 will have the same calendar as that of the year 1990?
a) 1995  b) 1997 c) 1996 d) 1992

16)  January, 1, 1992 was a Wednesday. What day of the week will it be on January 1,  1993 ?

17) Find the day of the week on 12th January, 1979.

18) Mahatma Gandhi was born 2nd October, 1869. The day of the week was ----

19) In July 2, 1985, it was Wednesday. The day of the week on July 2, 1984 was ----

20)  Today is 21st August. The day of the week is Monday. This is a leap year. What will be the day of the week on this day after 3 years?

Answer

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