The document discusses calendars and methods for determining the day of the week for a given date. It provides information on lunar and Gregorian calendars. It also gives examples of solving problems to determine the day of the week for dates in the past using the formula of dividing the total number of days by 7 and analyzing leap years.

1. Calendar
Ms.S.SWATHI SUNDARI, Assistant Professor of Mathematics, V.V.Vanniaperumal College For Women, Virudhunagar - 626001

2.  A Basic understanding of Time/Year Every year we celebrate new year on 1st Jan.
 This calculation started 2013 years ago.
 But ancient Indians had a deeper perspective and knowledge about time in relation to the entire cosmos.
 As we venture to celebrate the dawn of new year 2014, let us gain an understanding of this also.
 As per Lunar calendar new year is called as Yugadi (Yuga = a unit of time and Adi = beginning).
 This day signifies the birth of this Kali Yugam.
 According to this calculation we are in 5114th year and the new year will start in Mar/Apr every year.
 31st Mar 2014 is the Yugadi (New year day).

4. Ms.S.SWATHI SUNDARI, Assistant Professor of Mathematics, V.V.Vanniaperumal College For Women, Virudhunagar - 626001
⌘ 1 Week = 7 Days
⌘ 1 Year = 52 Weeks + 1 Odd Day (Extra Day)
⌘ Leap Year = 52 Weeks + 2 Odd Days (Extra Day)
⌘ Ordinary Year = 365 Days
⌘ Leap Year = 366 Days
⌘Ordinary Year ⇒ 28th Feb
⌘ Leap Year ⇒ 29th Feb

5. Ms.S.SWATHI SUNDARI, Assistant Professor of Mathematics, V.V.Vanniaperumal College For Women, Virudhunagar - 626001
No.of
Days
0 3 3 6 1 4 6 2 5 0 3 5
Months Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
No.of
Days
Day
0 Sun
1 Mon
2 Tue
3 Wed
4 Thu
5 Fri
6 Sat
Years Code
1600 – 1699 6
1700 – 1799 4
1800 – 1899 2
1900 – 1999 0
2000 – 2099 6

6. Ms.S.SWATHI SUNDARI, Assistant Professor of Mathematics, V.V.Vanniaperumal College For Women, Virudhunagar - 626001
Problem – 1
What was the day of the week on 26th Jan 1947?
Steps Consequences
• Take last two digits of the year 47
• Divide it by 4 and Take the Quotient 47/4, Q = 11
• Take the Date 26
• Take the number of the month 0
• Take the number of the year 0
(Add the above consequences) Total 84
• Divide it by 7 (Since, 1 week = 7 Days) Q = 12, R = 0
No.of
Days
0
Months Jan
No.of
Days
Day
0 Sun
1 Mon
2 Tue
3 Wed
4 Thu
5 Fri
6 Sat
Years Code
1600 – 1699 6
1700 – 1799 4
1800 – 1899 2
1900 – 1999 0
2000 – 2099 6
ANS : SUNDAY

7. Ms.S.SWATHI SUNDARI, Assistant Professor of Mathematics, V.V.Vanniaperumal College For Women, Virudhunagar - 626001
Problem – 2
What was the day of the week on 5th Oct 2016?
Steps Consequences
• Take last two digits of the year 16
• Divide it by 4 and Take the Quotient 16/4, Q = 4
• Take the Date 5
• Take the number of the month 0
• Take the number of the year 6
(Add the above consequences) Total 31
• Divide it by 7 (Since, 1 week = 7 Days) Q = 4, R = 3
No.of
Days
0
Months Jan
No.of
Days
Day
0 Sun
1 Mon
2 Tue
3 Wed
4 Thu
5 Fri
6 Sat
Years Code
1600 – 1699 6
1700 – 1799 4
1800 – 1899 2
1900 – 1999 0
2000 – 2099 6
ANS : WEDNESDAY

8. Ms.S.SWATHI SUNDARI, Assistant Professor of Mathematics, V.V.Vanniaperumal College For Women, Virudhunagar - 626001
Problem – 3
What was the day of the week on 29th Feb 2012?
Steps Consequences
• Take last two digits of the year 12
• Divide it by 4 and Take the Quotient 12/4, Q = 3
• Take the Date 29
• Take the number of the month 3
• Take the number of the year 6
(Add the above consequences) Total 53
• Divide it by 7 (Since, 1 week = 7 Days) Q = 7, R = 4
• Since 2012 is a leap year. So, 4 – 1 = 3
No.of
Days
3
Months Feb
No.of
Days
Day
0 Sun
1 Mon
2 Tue
3 Wed
4 Thu
5 Fri
6 Sat
Years Code
1600 – 1699 6
1700 – 1799 4
1800 – 1899 2
1900 – 1999 0
2000 – 2099 6
ANS : WEDNESDAY

9. Ms.S.SWATHI SUNDARI, Assistant Professor of Mathematics, V.V.Vanniaperumal College For Women, Virudhunagar - 626001
Problem – 4
What dates of May 2002 did Monday fall?
Steps Consequences
• Take last two digits of the year 2
• Divide it by 4 and Take the Quotient 2/4, Q = 0
• Take the Date 1
• Take the number of the month 1
• Take the number of the year 6
(Add the above consequences) Total 10
• Divide it by 7 (Since, 1 week = 7 Days) Q = 1, R = 3
No.of
Days
1
Months May
No.of
Days
Day
0 Sun
1 Mon
2 Tue
3 Wed
4 Thu
5 Fri
6 Sat
Years Code
1600 – 1699 6
1700 – 1799 4
1800 – 1899 2
1900 – 1999 0
2000 – 2099 6
Take the date, 1st May 2002

10. Ms.S.SWATHI SUNDARI, Assistant Professor of Mathematics, V.V.Vanniaperumal College For Women, Virudhunagar - 626001
Problem – 4
What dates of May 2002 did Monday fall?
Steps Consequences
• Take last two digits of the year 2
• Divide it by 4 and Take the Quotient 2/4, Q = 0
• Take the Date 1
• Take the number of the month 1
• Take the number of the year 6
(Add the above consequences) Total 10
• Divide it by 7 (Since, 1 week = 7 Days) Q = 1, R = 3
May,
1
2 3 4 5 6
Wed Thu Fri Sat Sun Mon
So, 1st May 2002 is Wednesday
So, 6+7 = 13
13+7 = 20
20+7 = 27
ANS : May 6, 13, 20, 27

11. Ms.S.SWATHI SUNDARI, Assistant Professor of Mathematics, V.V.Vanniaperumal College For Women, Virudhunagar - 626001
Problem – 5
Today is Monday, after 30 days it will be?
Steps Consequences
• Take the total number of days 30
• Divide it by 7 and Take the Remainder 30/7, Remainder = 2
• Take that Today’s Day and Add that
Remainder
Monday + 2 =
Wednesday
ANS : WEDNESDAY

12. Ms.S.SWATHI SUNDARI, Assistant Professor of Mathematics, V.V.Vanniaperumal College For Women, Virudhunagar - 626001
Problem – 6
Jan 4, 2016 falls on Monday, What day of the week does Jan 4, 2017 lies?
Steps Consequences
• Take the Date Jan 4, 2016 - Monday
• Check whether it is Leap year / Ordinary Year 2016 – Leap Year
• Add Odd Day to it (+ 2) Monday + 2 = Wednesday
1 Normal Year 1 Odd Day
1 Leap Year 2 Odd Days
ANS : WEDNESDAY