My Tax & Diary

CALENDAR - IMPORTANT FACTS AND FORMULA


Undertand the following points it will help in finding the day of the week on a particular given date the process of finding it lies on obtaining the number of odd days.

Odd Days : Number of days more than the complete number of weeks in a given

Period ., is the number of odd days during that period.

Leap Year: Every year which is divisible by 4 is called a leap year.

Thus each one of the years 1988, 1992, 1996, 2004, 2008, 2012, 2016 etc. is a leap year.

A leap year has 366 days.

Every 4th century is a leap year but no other century is a leap year. thus each one of 400, 800, 1200,' 1600, 2000, etc. is a leap year.

And none of 1900, 2010, 2020, 2100, etc. is a leap year.

An year which is not a leap year is called an ordinary year.

An ordinary year has 365 days.

Counting of Odd Days:

i) ordinary year = 365 days = (52 weeks + 1 day).

i.e An ordinary year has 1 odd day.

ii) leap year = 366 days = (52 weeks + 2 days).

i.e. A leap year has 2 odd days.

iii)100 years = 76 ordinary years + 24 leap years

which is = [(76 x 52) weeks + 76 days) + [(24 x 52) weeks + 48 days]

which is = 5200 weeks + 124 days = (5217 weeks + 5 days).

Please remember

100 years contain 5 odd days.

200 years contain 10 and therefore 3 odd days.

300 years contain 15 and therefore 1 odd day.

400 years contain (20 + 1) and therefore 0 odd day.

Similarly, each one of 800, 1200, 1600, 2000, etc. contains 0 odd days.

Remark: (7n + m) odd days, where m < 7 is equivalent to m odd days. Thus, 8 odd days and 1 odd day etc.

The following example will help you to understand how to find the day of the week

Wbat was the day of the week on, 16th July, 1776?

16th July, 1776 = (1775 years + Period from 1st Jan., 1776 to 16th July, 1776)

Let Count the odd days :

1600 years have 0 odd day. 100 years have 5 odd days.

75 years = (18 leap years + 57 ordinary years)

= [(18 x 2) + (57 x 1)] odd days = 93 odd days

= (13 weeks + 2 days) = 2 odd days.

That means : 1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day.

The days of month - Jan. Feb. March April May June July 31 + 29 + 31 + 30 + 31 + 30 +16 = 198days

It comes to = (28 weeks + 2 days) =2days

Total number of odd days = (0 + 2) = 2.

Required day was "Tuesday"











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