calendar problems

Solving Calender Problems

Important formula for solving calender problem

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 4^th century is a leap year and no other century is a leap year.Note: A leap year has 366 days.
   Examples:
   1. Each of the years 1948, 2004, 1676 etc. is a leap year.
   2. Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.
   3. 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.

6. To learn more about calender problem click the link below

[youtube https://www.youtube.com/watch?v=74YD9K5Q_04?version=3&rel=1&fs=1&showsearch=0&showinfo=1&iv_load_policy=1&wmode=transparent]

Solve the calender problem in 30 sec click the link below

[youtube https://www.youtube.com/watch?v=Ig3m365yJws?version=3&rel=1&fs=1&showsearch=0&showinfo=1&iv_load_policy=1&wmode=transparent]

Practice your skills here

Ex. What was the day of the week on 20 may, 1985 ?

Solution : Here Number of odd days in 1600 years = 0

Number of odd days in 300 years from 1600 to 1900 = 5*3 = 2 week + 1 odd day= 1 odd day

Number of odd days in 84 years= 21 leap year + 63 days = 21*2 + 63*1 = 105 days = 0 odd days

Number of odd days in 20 may = 31 days of Jan. + 28 days of feb + 31 days of mar. + 30 days in april + 20 days in may = 140 days = 0 odd day

So total number of odd days = 0+1+0+0=1 = Monday

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Ex. Prove that calendar for the year 2009 will serve for the year 2015.

Solution : for this sum of odd days from 2009 to 2014 should be zero.

Year	2009	2010	2011	2012	2013	2014
Odd day	1	1	1	2	1	1

Sum of odd days = 1+1+1+2+1+1=7= 1 week + 0 odd days

So, both dates 1.1.2009 and 1.1.2015 will be on same day , so calendar for the year 2009 will serve for the year 2015

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Ex. On what date of Feb. 2007 did Saturday fall ?

Solution : For this find the day of 1.2.2007

1600+400 years has 0 odd days

From 2001 to 2006 there are 1 leap years + 5 ordinary years

So number of odd days = 1*2 + 5*1 = 2 + 5 = 7 = 1 week = 0 odd day

Now from 1.1.2007 to 1.2.2007 number of days = 32 = 4 weeks + 4 odd days = 4 odd days

So, total number of odd days = 4, so 1.2.2007 will be thrusday

Now saturday will be on 3.2.2007

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Ex. Today is tuesday. After 72 days, it will be ?

Solution : Tuesday will be repeated after each 7 days so, after at 70 day it will also be tuesday, so at 72 th day it will be friday

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