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 ordinary year has 365 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).

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.

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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