ThePrismSolutions

ThePrismSolutions

CALENDAR

Odd Days:

Number of days more than the complete number of weeks in a given

Period

is the number of odd days during that period.

LeapYear:

Every year which is divisible by 4 is called a leap year. Thus each one of the years 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 1900, 2010, 2020, 2100, etc. is a leap year.

An year which is not a leap year is called an ordinary year.

(I )An ordinary year has 365 days.

(II) A leap year has 366 days.

Counting of Odd Days:

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

:. An ordinary year has 1 odd day.

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

:. A leap year has 2 odd days.

iii)100 years = 76 ordinary years + 24 leap years

= [(76 x 52) weeks + 76 days) + [(24 x 52) weeks + 48 days]

= 5200 weeks + 124 days = (5217 weeks + 5 days).

:. 100 years contain 5 odd days.

200 years contain 10 and therefore 3 odd days.

300 years contain 15 and therefore 1 odd day.

400 years contain (20 + 1) and therefore 0 odd day.

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

Remark: (7n + m) odd days, where m < 7 is equivalent to m odd days.

Thus, 8 odd days =1 odd day etc.

No of odd days  	Day
	 0		Sun
	 1  		Mon
	 2		Tues
	 3		Wed
	 4		Thur
	 5		Fri
	 6	        Sat



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