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Important Formulas

 

(I). 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.

(II). 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.

Note: A leap year has 366 days.

Examples:

  1. Each of the years 1948, 2004, 1676 etc. is a leap year.
  2. Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.
  3. None of the years 2001, 2002, 2003, 2005, 1800, 2100 is a leap year.

 

(III). Ordinary Year:

The year which is not a leap year is called an ordinary year. An ordinary year has 365 days.

(IV). Counting of Odd Days:

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

1 ordinary year has 1 odd day.

(II). 1 leap year = 366 days = (52 weeks + 2 days)

1 leap year has 2 odd days.

(III). 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.

Number of odd days in 200 years = (5 * 2) = 3 odd days.

Number of odd days in 300 years = (5 * 3) = 1 odd day.

Number of odd days in 400 years = (5 * 4 + 1) = 0 odd day.

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

(V).  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.