1. Odd Days:
We are
supposed to find the day of the week on a given date.
In a given
period, the number of days more than the complete weeks are called odd days.
2. Leap Year:
(ii). Every
4th century is a leap year and no other century is a leap year.
Note: A leap year has 366 days.
Examples:
i. Each of the years 1948, 2004, 1676 etc. is a
leap year.
ii. Each of the years 400, 800, 1200, 1600, 2000
etc. is a leap year.
iii. None of
the years 2001, 2002, 2003, 2005, 1800, 2100 is a leap year.
3.
Ordinary Year:
The year
which is not a leap year is called an ordinary years. An ordinary year
has 365 days.
4. Counting of Odd Days:
Therefore 1 ordinary year has 1 odd
day.
2. 1
leap year = 366 days = (52 weeks + 2 days)
Therefore 1 leap year has 2 odd
days.
3. 100
years = 76 ordinary years + 24 leap years
= (76 x 1 + 24 x 2) odd days = 124 odd days.
= (17 weeks + days) ≡ 5 odd days.
Therefore Number of odd
days in 100 years = 5.
Number of odd days in 200 years
= (5 x 2) ≡ 3 odd days.
Number of odd days in 300 years
= (5 x 3) ≡ 1 odd day.
Number of odd days in 400 years
= (5 x 4 + 1) ≡ 0 odd day.
Similarly, each one of
800 years, 1200 years, 1600 years, 2000 years etc. has 0 odd days.
5. Day of the Week Related to Odd Days:
No. of days:

0

1

2

3

4

5

6

Day:

Sun.

Mon.

Tues.

Wed.

Thurs.

Fri.

Sat.

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