Odd Days:
We are supposed to find the day of the week on a given date.
For this, we use the concept of ‘odd days’.
In a given period, the number of days more than the complete weeks are called odd days.
· Leap Year:
(i). Every year divisible by 4 is a leap year, if it is not a century.
(ii). Every 4^{th} century is a leap year and no other century is a leap year.
Note: A leap year has 366 days.
Examples:
 Each of the years 1948, 2004, 1676 etc. is a leap year.
 Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.
 None of the years 2001, 2002, 2003, 2005, 1800, 2100 is a leap year.
· Ordinary Year:
The year which is not a leap year is called an ordinary years. An ordinary year has 365 days.
· Counting of Odd Days:
 1 ordinary year = 365 days = (52 weeks + 1 day.)
1 ordinary year has 1 odd day.
 1 leap year = 366 days = (52 weeks + 2 days)
1 leap year has 2 odd days.
 100 years = 76 ordinary years + 24 leap years
= (17 weeks + days) 5 odd days.
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.
· 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.

SOLVED EXAMPLES
1. What was the day of the week on, 16th July, 1776 ( Tuesday)
2. What was the day of the week on 16th August, 1947? (Saturday)
3. What was the day of the week on 16th April, 2000? (Sunday )
4. On what dates of Jull.2004 did Monday fall? (5^{th} , 12^{th} , 19^{th}and 26^{th} )
5. Prove that the calendar for the year 2008 will serve for the year 2014.
6. Prove that any date in March of a year is the same day of the week corresponding date in November that year.
EXERCISE
1. January 1, 2004 was Thursday. What day of the week lies on Jan. 1, 2005?
2. On 8th March, 2005 Wednesday falls. What day of the week was it on 8th March, 2004?
3. The calendar for the year 2005 is the same as for the year:
i. 2010 ii. 2011 iii. 2012 iv. 2013
4. On what dates of April, 2001 did Sunday fall?
A. 1^{st} , 8^{th} , 15^{th}, 22^{nd} , 29^{th} B. 2^{nd} , 9^{th} , 16^{th}, 23^{rd} , 30^{th}
C. 4^{th} , 11^{th} , 18^{th}, 25^{th} D. 3^{rd} , 10^{th} , 17^{th} , 24^{th}
5. What will be the day of the week on 1^{st} January, 2010?
6. What was the day of the week on 17th June, 1998?
7. What was the day of the week on 28th May, 2003?
8. Today is Friday. After 62 days, it will be:
9. The last day of a century cannot be:
i. Monday ii. Wednesday iii. Friday iv. Tuesday
10. The first Republic Day of India was celebrated on 26^{th} January, 1950. It was: