Main concepts :
a) Odd Days : The number of days more than the complete number of weeks in a given period is number of odd days during that period.
b) Leap year : Every year which is divisible by 4 is called a leap year. Thus each one of he year 1992, 1996, 2004, 2008, 2012 etc is a leap year.
Every 4th century is a leap year but no other century is a leap year thus each one of 400, 800, 1200, 1600, 2000 etc is a leap year. None of the 1900, 2010, 2020, 2100 etc is a leap year. An year which is not a leap year is called Ordinary year.
c) An ordinary year has 365 days.
d) A leap year has 366 days.
e) Counting of odd days :
i)1 ordinary year = 365 days =52 weeks+1 day,Therefore An ordinary year has 1 Odd day.
ii) One leap year = 366 days =52 weeks+2 days, Therefore a leap year has 2 Odd days.
iii) 100 years = 76 ordinary years + 24 leap years
= [(76*52) weeks +76 days]+[(24*52)weeks+48 days]
= 5200 weeks + 124 days=[5217 weeks+5 days]
therefore 100 years contain 5 odd days
iv)200 years contain 10(1 week + 3 days), i.e 3 odd days
v)300 years contain 15(2 weeks + 1 day), i.e 1 odd day
vi)400 years contain (20+1), i.e 3 weeks,so 0 Odd days
similarly each one of 800,1200,1600,2000,etc contains o odd days.
Note: (7n+m) odd days , where m less than or equal to 7 is equivalent to m odd days, thus, 8 odd days = 1 odd day etc.
f) Some codes o remember the months and weeks:
a) Week
Sunday - 1
Monday - 2
Tuesday - 3
Wednesday - 4
Thursday - 5
Friday - 6
Saturday - 0
b) Month
Jan - 1 July - 0
Feb - 4 Aug - 3
Mar - 4 Sep - 6
Apr - 0 Oct - 1
May - 2 Nov - 4
June - 5 Dec - 6
