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Important Points :
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 4th century is a leap year and no other century 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
= (76 x 1 + 24 x 2) odd days = 124 odd days.
= (17 weeks + days) = 5 odd days.
* Number of odd days in 100 years = 5 odd days
* 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 (Assuming that 1AD January 1st is a Sunday):
|Number of Odd Days||0||1||2||3||4||5||6|
|Day of the week||Sunday||Monday||Tuesday||Wednesday||Thursday||Friday||Saturday|