What is a Calendar? 
A calendar is an instrument which is used to keep, indicate and organize the days in a year. We follow the Gregorian calendar which is also called as the Christian calendar or the Western calendar. The Western calendar is the widely used internationally as the civil calendar. The Gregorian calendar starts on 1st January and ends on 31st December. The Gregorian calendar is named after Pope Gregorian XIII, who introduced the calendar in October 1582. 

Ordinary year – An ordinary year has 365 days.

Leap year – A leap year has 366 days.

 

The difference between an ordinary year and a leap year is that a leap year has one extra day, designated as 29th February. A leap year occurs every four years, to keep the calendar in alignment with the earth’s revolution around the sun. Earth takes 365 ¼ days to complete one revolution. Hence, to compensate 1/4th day or 6 hours in the calendar we have a leap year.Therefore, a year cannot be a leap year if it is not divisible by 4 or 400.

 

For example – 1700, 1800, 1900 are not a leap year because it is not divisible by 400.

1600, 2000, 2400 are leap years because they are divisible by 400

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1.    Questions that ask you to find the day of the week for the given date when some other date or day is specified.

2.    Questions that ask you to find the day of the week for the given date when no other date or day is specified.

 

Calendar Problems can be solved using the concept of odd days

Odd Days: In a given time period, the number of days that are more than the weekly cycle are called odd days.

For example: 10 days = 1 week + 3 days.

Then the extra 3 days become odd days.

Likewise,

15 days = 2 weeks + 1 day (1 odd day)

30 days = 4 weeks + 2 days (2 odd day)

Ordinary years = 365 days = 52 weeks + 1 day (1 odd day)

Leap year 366 days = 52 weeks + 2 days (2 odd day)

Therefore, an ordinary year has 1 odd day and a leap year has 2 odd days.

 

1st January 0001 A.D à Monday (Reference Chart)  

*Sunday is taken as the reference point.

 

Number of odd days for longer Periods 
 

è Calculate the Number of Odd days for the 1st Century – 100 years:
Solution:
Step 1:

In the first century, there were 24 leap years. (100/4 = 25. Since 100th year is not divisible by 400 we deduct 1 year)

Ordinary years = 76

 

Number of odd days = 76 x 1(Since ordinary years have 1 odd day) + 24 x 2 (Since leap years have 2 odd days)

= 76 + 48

= 124

 

124 = 17 weeks + 5 days

Therefore, there are 5 odd days

Hence, the last day of 1st century i.e. 31st December is Friday (according to reference chart)

 

è Calculate the number of odd days for the first 200 years:
Solution:

Odd days = 5 x 2 (Since the second century has the same number of odd days)

= 10 odd days

 

10 odd days = 1 week + 3 days

Therefore there are 3 odd days in the first 200 century.

Hence, the last day of 200 years i.e. 31st December is Wednesday (according to reference chart)

Calendar Problem Solved using Smart Tricks
Problem: Which day of the week was 15th August 1947?

Solution: Step 1: 
To simplify the calculation, break the years 

1600 years + 300 years + 46 years + (January – July) + 15 days

 

Step 2: 
Calculate the odd days for the years 
1600 years = 0 odd days

300 years = 1 odd day

46 years = (35 ordinary years + 11 leap years)
 = (35 odd days + 22 odd days) = 57 odd days = 1 odd day

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

 

 Adding the odd days = 0 + 1 + 1 + 3 + 0 + 3 + 2 + 3 + 2 + 3 + 1

= 19 odd days

= 2 weeks + 5 odd days

= 5 odd days

Therefore, 15th August 1947 was a Friday, since 5 odd days indicate Friday.