Problems on Calendar

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