1. Odd Days

In a given period, the number of days more than the complete weeks are called odd days.

2. 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:
  • 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.

3. Ordinary Year

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

4. Counting of Odd Days

1. 1 ordinary year = 365 days = (52 weeks + 1 day).
   • $\therefore$ 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
   • $= (76 \times 1 + 24 \times 2)$ odd days = 124 odd days.
   • $= (17 \text{ weeks} + 5 \text{ days}) \rightarrow$ 5 odd days.
   • Number of odd days in 100 years = 5.
   • Number of odd days in 200 years = $(5 \times 2) \rightarrow$ 3 odd days.
   • Number of odd days in 300 years = $(5 \times 3) \rightarrow$ 1 odd day.
   • Number of odd days in 400 years = $(5 \times 4 + 1) \rightarrow$ 0 odd days.
   • Similarly, each one of 800 years, 1200 years, 1600 years, 2000 years etc. has 0 odd days.