Calendar
– Formulas
1. 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.
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:
i.
Each of
the years 1948, 2004, 1676 etc. is a leap year.
ii.
Each of
the years 400, 800, 1200, 1600, 2000 etc. is a leap year.
iii.
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 years. An ordinary year has 365 days.
4.
Counting
of Odd Days:
1. 1 ordinary year = 365 days = (52
weeks + 1 day.)
= 1 ordinary year has 1 odd
day.
2. 1 leap year = 366 days = (52
weeks + 2 days)
= 1 leap year has 2 odd days.
3. 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 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.
5.
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. |