Calendar Math Tricks

• Ordinary Year

A year having 365 days is called an Ordinary Year, which has

(52 complete weeks + 1 Extra/Odd day)

• Leap Year

A Leap Year has 366 days (including 29th of February) and

(52 complete weeks + 2 Extra/Odd days)

1. A leap year is divisible by 4, like 1984, 1988, 2008, 2012 etc.
2. A century is divisible by 400, like 1600, 2000, 2400 etc.
3. Centuries like 1700, 1800 are not divisible by 400.

• Odd Days

• Number of odd days in Ordinary Year

365 days = (52 weeks*7) + 1 odd day.

• Number of days in a Leap Year

366 days = (52*7) + 2 odd days.

• Number of odd days in a Century (100 year)

100/4 = 24 leap year + (100 - 24 = 76) 76 ordinary year.

(76*1 + 24*2)[since ordinary year has 1 odd day and leap yeas has 2 odd days]

124 days = 7 week*17 + 5 odd days.

• Number of Odd days in 200 year

= 5*2 [since 100 year has 5 odd days and here it is 200 year]

10 odd days = 1 week + 3 odd days.

• Number of Odd days in 300 year

5*3 = 15 odd days 

=2 week + 1 odd day.

• Number of Odd days in 400 year

5*4 + 1 = 21 odd days

=3 weeks + 0 odd days.

[since 400th year is a leap year, so 1 more day is added]