PROBLEMS ON CALENDARS - Concept Part 2
Finding the day of the week on a particular day when the reference
date is given:
Calculate the "odd
days" between the given and reference dates.
Exclude the reference
day but include the target date in your calculation.
Example :
If January 1st,
2023 is a Sunday, March 14th, 2023 will be?
Reference Date: January 1, 2023
(Assume it's a Sunday)
Given Date: March 14, 2023
Number of days between the
two dates :
Counting the number of days between
January 1 and March 10 (excluding January 1):
Number of days=30(January)+28(February)+14(March)=72
Count the number of odd
days :
The number of odd days in 72 days = 10
weeks + 2 extra days = 2 odd days
The target date (March 12) is after
the reference date (January 1), so we are expecting a day "ahead" of
the reference day.
Find the Day of the Week
on the Target Date
Since there are 2 odd days, we count
forward from Sunday:
Sunday + 2 = Tuesday
So, March 14th, 2023, falls on a
Tuesday.
In summary, if January 1, 2023, is a
Sunday, then March 14, 2023, is a Tuesday
Example 2 :
If July 1, 2024, is a
Thursday, then 12th April 2024 is ?
Reference Date: July 1, 2024 (Assume
it's a Thursday)
Target Date: April 12, 2024
Number of days between the two dates:
Counting the number of days between
July 1 and April 12 (excluding July 1):
Number of days = 30 (June) + 31 (May)
+ 19 (April) = 80
Count the number of odd days:
The number of odd days in 80 days = 11
weeks and 3 days= 3 odd days
Find the Day of the Week on the Target
Date:
Since there are 3 odd days, we count
backward from Thursday:
Thursday - 3 = Monday
So, May 12th, 2024, falls on a Monday.
Predicting Identical Calendars in Different
Years(Repetition
of the calendar )
For any ( leap year + 1) year :
Let
us take an example, 2005
Year
2005 2006 2007 2008
2009 2010
Odd
days 1
1 1
2 1
1
Since
the number of odd days is 7, so calendars of 2005 and 2011 will be the same for
the whole year.
Any (leap year +1), the same calendar will occur after 6
years.
2005
+ 6 =2011
For any ( leap year + 2) year :
Let
us take an example, 2006
Year
2006 2007
2008 2009 2010 2011
2012 2013 2014
2015 2016
Odd days
1 1
2 1
1 1 2
1 1 1 2
Since
the number of odd days is 14 (i.e. 0), so calendars of 2006 and 2017 will be the
same.
Any ( leap year + 2), the same calendar will occur after 11
years.
2006
+ 11 =2017
For any ( leap year + 3) year :
Let
us take an example, 2007
Year
2007 2008
2009 2010 2011 2012 2013 2014 2015 2016
2017
Odd
days 1 2
1 1 1 2
1 1 1
2 1
Since
the number of odd days is 14, so calendars of 2007 and 2018 will be the same
for the whole year.
Any ( leap year +3), the same calendar will occur after 11
years.
2007
+ 11 =2018
Same calendar for a leap Year :
The calendar of a leap year repeats itself
after 28 years.
So, to find the year with the same calendar as a given leap
year, simply add 28 to that year.
For example, the calendar of 2004 is the same as the calendar
of 2004 + 28 = 2032.
The same Calendars of months in a year
Leap Year: January & July, February & August.
Non-Leap Year: January & October, February & March
Any year, leap or non
leap year: March & November, April &
July, September & December
Finding the day of the week on a particular date:
How to find the day of
the week on a given date :
To find the day of the week on a date,
we need to find odd days right from the 1st January 1 A.D. to the
date given. We add up the odd days of the complete centuries, the completed
years of the present century and the completed quarters, the completed months
of the current quarter, and the number of days of the current month.
Example: Find out the
day of the week on November 8th, 2015.
Explanation:
Period Number
of odd days
First 2000 years (5 x 400 years)
0
14 years (3 leap+11 normal years) 17
2015. First quarter Jan, Feb, Mar 6
2015, 2nd quarter Apr, May, June 0
2015, Third quarter July, Aug, September 1
2015 October 31 days 3
2015 November up to 8th 1
-------------------------------------------------------------------------------------
Total 28
NUMBER OF ODD DAYS
0
Number of odd days =0
This means that the day of the week on
November 8th is Sunday.
Number of odd days Day of the week
0
Sunday
1
Monday
2
Tuesday
3
Wednesday
4
Thursday
5
Friday
6
Saturday
Important Points :
1.
The last day of a century cannot be either
a Tuesday, Thursday, or Saturday.
2.
The first day of the
century cannot be either Wednesday, Friday, or Sunday
