CALENDAR
Calendar is a chart or series of pages showing the days, weeks, and months of a particular year, or giving particular seasonal information.
We follow the Gregorian calendar which is also called as the Christian Calendar or the Western calendar
The Western calendar is the widely used in international.
Note:-The basic thing to remember to solve calendar problems.
Example.1.:-What as the day of the week on 15th August 1947( Independence day).
Explanation:-Counting of odd day
Number of odd day in 1600 years = 0
Number of odd day in 300 years = 5*3 = 15 days = 2 weeks + 1
Number of odd day in 46 years = 11 leap years + 35 Ordinary years
= 11*2 + 35*1 = 57 odd days
=8*7 + 1 = 1 odd day
Odd days in 1946 years = 0+1+1 = 2.
In 1947th year
January = 31 days = 3 odd days
Number of odd day in 1600 years = 0
Number of odd day in 300 years = 5*3 = 15 days = 2 weeks + 1
Number of odd day in 49 years = 12 leap years + 37 Ordinary years
= 12*2 + 37*1 = 61 odd days
=8*7 + 5 = 5 odd days
Odd days in 1946 years = 0+1+5 = 6.
In 1950th year
January = 26 days = 5 odd days
Number of odd day in 1600 years = 0
Number of odd day in 200 years = 5*2 = 10 days = 1 week + 3
Number of odd day in 68 years = 17 leap years + 51 Ordinary years
= 17*2 + 51*1 = 85 odd days
=12*7 + 1 = 1 odd day.
Odd days in 1869 years = 0+3+1 = 4.
In 1869th year
January = 31 days = 3 odd days
e required day was Saturday.
Calendar is a chart or series of pages showing the days, weeks, and months of a particular year, or giving particular seasonal information.
We follow the Gregorian calendar which is also called as the Christian Calendar or the Western calendar
The Western calendar is the widely used in international.
Note:-The basic thing to remember to solve calendar problems.
Odd Days:- In a given time period, the number of remaining days more than complete weeks are called odd days.
Ordinary year:-An ordinary year has 365 days.
Leap year :- A leap year has 366 days.
(1) Every year divisible by 4 is a leap year,if it is not century.
(2) Every century divisible by 400 is a leap year.
As 400,800,1200,1600,2000 etc.
Counting of odd days:-
(1). One ordinary year = 365 days = 52*7+1 days
=52 weeks + 1 day.
Hence 1 ordinary year has 1 odd day.
(2). One leap year = 366 days = 52*7+2 days
=52 weeks + 2 days.
Hence 1 leap year has 2 odd days.
(3). 100 years = 76 ordinary years + 24 leap years
=76*1 odd days + 24*2 odd days
= 126 odd days = 17*7 + 5 days.
Hence 100 years has 5 odd days.
(4). 200 years = 5*2 odd days.=10 odd days
=1 week + 3 odd days.
(5). 300 years = 5*3 odd days.=15 odd days
=2 weeks + 1 odd day.
(6). 400 years = 5*4 odd days.+1 odd day=21 odd days
=3 weeks = 0 odd day.
Table of week related to odd day
Number of odd days
|
Day
|
0
|
Sunday
|
1
|
Monday
|
2
|
Tuesday
|
3
|
Wednesday
|
4
|
Thursday
|
5
|
Friday
|
6
|
Saturday
|
Example.1.:-What as the day of the week on 15th August 1947( Independence day).
Number of odd day in 1600 years = 0
Number of odd day in 300 years = 5*3 = 15 days = 2 weeks + 1
Number of odd day in 46 years = 11 leap years + 35 Ordinary years
= 11*2 + 35*1 = 57 odd days
=8*7 + 1 = 1 odd day
Odd days in 1946 years = 0+1+1 = 2.
In 1947th year
January = 31 days = 3 odd days
February = 0 odd days
March = 31 days = 3 odd
days
April = 30 days = 2 odd
days
May = 31 days = 3 odd days
June = 30 days = 2 odd
days
July = 31 days = 3 odd
days
August = 15 days = 1 odd
day
Total number of odd days= 2+3+0+3+2+3+2+3+1=19 = 2*7 + 5
= 5
Hence the required day was Friday.
Example.2.:-What as the day of the week on 26th January 1950.
( Constitutional Implemented day)
Counting of odd dayNumber of odd day in 1600 years = 0
Number of odd day in 300 years = 5*3 = 15 days = 2 weeks + 1
Number of odd day in 49 years = 12 leap years + 37 Ordinary years
= 12*2 + 37*1 = 61 odd days
=8*7 + 5 = 5 odd days
Odd days in 1946 years = 0+1+5 = 6.
In 1950th year
January = 26 days = 5 odd days
Total number of odd days= 6 + 5=11 = 1*7 + 4
= 4
Hence the required day was Thursday.
Example.3.:-What as the day of the week on 2nd October 1869 ( Bapu Jayanti).
Counting of odd dayNumber of odd day in 1600 years = 0
Number of odd day in 200 years = 5*2 = 10 days = 1 week + 3
Number of odd day in 68 years = 17 leap years + 51 Ordinary years
= 17*2 + 51*1 = 85 odd days
=12*7 + 1 = 1 odd day.
Odd days in 1869 years = 0+3+1 = 4.
In 1869th year
January = 31 days = 3 odd days
February = 0 odd days
March = 31 days = 3 odd days
April = 30 days = 2 odd days
May = 31 days = 3 odd days
June = 30 days = 2 odd days
July = 31 days = 3 odd days
August = 31 days = 3 odd days
September = 30 days = 2 odd days
October = 2 days
Total number of odd days= 4+3+0+3+2+3+2+3+3+2+2=27 = 3*7 + 6
Alternative short trick to find calendar
Note:-Remember these things
Century code table
|
5th
|
6th
|
7th
|
8th
|
9th
|
10th
|
11th
|
12th
|
13th
|
14th
|
15th
|
16th
|
17th
|
18th
|
19th
|
20th
|
|
4
|
2
|
0
|
6
|
4
|
2
|
0
|
6
|
4
|
2
|
0
|
6
|
4
|
2
|
0
|
6
|
Month code
|
Jan
|
Feb
|
Mar
|
Apr
|
May
|
Jun
|
Jul
|
Aug
|
Sep
|
Oct
|
Nov
|
Dec
|
|
1
|
4
|
4
|
0
|
2
|
5
|
0
|
3
|
6
|
1
|
4
|
6
|
Month code
|
Sun
|
Mon
|
Tues
|
Wed
|
Thurs
|
Fri
|
Sat
|
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
Formula
Remaining odd day=[Date+Month+Year+Leap Year+Century]/7
Example.1.:-What as the day of the week on 15th August 1947( Independence day).
Remaining odd day=[15+3+47+11+0]/7 = 76/7 = 6
Hence the required day was Friday.
e required day was Saturday.
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