This document discusses calendars and methods for determining the day of the week for a given date. It provides information on odd days in weeks, months, years and centuries. It also describes the logical method and using month codes to calculate the day of the week by determining the net odd days from a reference date. An example calculation is shown to find the day of the week for April 21, 1987 by working through the odd days until that year and applying the month code.

1. Alosies George
IIM Calcutta
director@georgeprep.com
+91- 9985-372371
Calendars
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2. Calendars
 Odd Days
• No of days more than complete weeks in a given period
• Remainder [(no of days)/7]
 Leap Year – A year with 366 days
• For century Years – divisible by 400
• For non century years – divisible by 4
 Ordinary Year – A year with 365 days
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3. Odd days calculation
Weeks
0 odd days
Months
Depending on the month
Years
Ordinary Year – 1 odd day(365 =52*7+1)
Leap year – 2 odd days (366=52*7+1)
Centuries
0001 AD – 0100 AD = 100 years( 76 ordinary + 24 leap years)= 5 odd days
0101 AD – 0200 AD = 100 years( 76 ordinary + 24 leap years) = 5 odd days
0201 AD – 0300 AD = 100 years( 76 ordinary + 24 leap years) = 5 odd days
0301 AD – 0400 AD = 100 years( 75 ordinary + 25 leap years) = 6 odd days
Every 400 hundred years
0001AD – 0400 AD = 0 odd days (Hence the calendar repeats)
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4. Basic rules
 1st Jan AD – Monday. We take the day before that( the 0th day)
to be Sunday and start our odd day calculations from there.
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5. Finding a day when a reference date is
given
A. If today is Wednesday. What day of the week will be 57 days from now?
B. If 21 April 1987 is a Tuesday. What day was
1. 15th April 1987
2. 15th November 1987
3. 26th December 1987
4. 2nd January 2025
5. 2nd January 1025AD
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6. Finding a day when a reference date is given
Which of the following years will have the exact same calendar as
2010?
1. 2013
2. 2014
3. 2015
4. 2016
5. None of these
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7. Finding a day when a reference date is not given
1. Using codes with logic
2. Doomsday Algorithm
3. Zeller’s Rule
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8. Logical Method
 What day of the week is 21 April 1987?
Till Odd days
1600 0
1900 ( 3 centuries) 5+5+5 = 1
1986 86+86/4 = 2+21=2
31st March 1987 3+0+3= 6
21st April 1987 21 = 0
Net Odd days 2
Day Odd Days
Sunday 0
Monday 1
Tuesday 2
Wednesda
y
3
Thursday 4
Friday 5
Saturday 6Answer : Tuesday (odd days =
2)
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9. Using Month Codes
 What day of the week is 21 April 1987?
Till Odd days
Yy and mm
(yy-1) calculation 86 + [86/4] = 2
MM Code For April, it is 6
CC code For 19, it is 1
dd 21=0
Net Odd days 2
Day Odd Days
Sunday 0
Monday 1
Tuesday 2
Wednesday 3
Thursday 4
Friday 5
Saturday 6
Answer : Tuesday (odd days = 2)
Ja F M A M Jn Jl A S O N D
0 3 3 6 1 4 6 2 5 0 3 5
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Century Odd days
4n + 1 5
4n + 2 3
4n + 3 1
4n 0
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