Solutions for Calendars

1.  What was the day of the week on 28^th may 2006?

    28%7=0 odd days

    May=1 odd day

    2006=2000+5 therefore there are 4 non leap years 
     and 1 leap year, 
     So 6 odd days

     So, (0+1+6) %7=0. 
     Therefore 28^th may 2006 is Sunday.

2.  On what dates of June 2015 did Friday fall?

    Let us consider 1st June 2015

    1%7=1 odd day

    June=4 odd days

    2015=(2000+14 ) therefore there are 11 non leap years 
     and 3 leap year, 
    So 17 odd days

    So, (1+4+17) %7=22%7=1. Therefore it is Monday.

    From this we can say that 5^th, 12th, 19^th, 26th  June 2015  
    are Fridays

3.  What was the day of the week on 30^th march 2012?

    30%7=2 odd days

    March=3 odd days

    2012=(2000+11) therefore there are 9 non leap years 
     and 2 leap year, 
     So 13 odd days

     So,  (2+3+13) %7 = 18%7 =  4 odd days.

    Since 30^th march 2012 is in leap year we have  1 odd day in extra. 
    Therefore 5 odd days and it is Friday.

4.  The starting day of the non leap year is Monday then
     what was the ending day of the same year?

      A non leap year always starts and ends with same day so Monday.
      ( 365 days= 52 weeks and 1 odd day)

5.  Jan 1^st 2015 was Thursday. What day of the week lies on Jan 1^st 2016?

     As 2015 is a non leap year so the year starts and ends with same day
      i.e. Thursday. So Jan 1^st 2016 is Friday.

6.  The calendar for the year 1993 will be the same for the year?

    1993- Non leap year =1%7=1 odd day

    1994- Non leap year = 2%7=2 odd days

    1995- Non leap year =3%7=3 odd days

    1996- Leap year =5%7=5 odd days

    1997- Non leap year =6%7=6 odd days

    1998- Non leap year =7%7=0 odd day

    1999 is same as 1993

7. The calendar for the year 1996 will be the same for the year?

     1996= 2 odd days =2%7=2

     1997= 1 odd day = 3%7=3

     1998= 1 odd day=4%7=4

     1999= 1 odd day=5%7=5

     2000=2 odd days=7%7=0

     2001= 1 odd day=1%7=1

     2002= 1 odd day=2%7=2 
     But 2002 is not leap year so the calendar will not be 
     the same as 1996
     2003= 1 odd day=3%7=3

     2004= 2 odd days=5%7=5

     2005=1 odd day=6%7=6

     2006= 1 odd day=7%7=0

    2007= 1 odd day=1%7=1

    2008= 2 odd days=3%7=3

    2009= 1 odd day=4%7=4

    2010=1 odd day=5%7=5

    2011= 1 odd day=6%7=6

    2012= 2 odd days=8%7=1

    2013= 1 odd day=9%7=2
    But 2013 is not leap year so the calendar will not be 
    the same as 1996
    2014=1 odd day=10%7=3

    2015= 1 odd day=11%7=4

    2016= 2 odd days=13%7=6

    2017= 1 odd day=14%7=0

    2018=1 odd day=1%7=1

    2019= 1 odd day=2%7=2 
   But 2019 is not leap year so the calendar will not be
    the same as 1996

   2020= 2 odd days=4%7=4

   2021= 1 odd day=5%7=5

   2022=1 odd day=6%7=6

   2023= 1 odd day=7%7=0

   2024 is leap year so the calendar will be the same as 1996

8.  The calendar for the year 2007 will be the same for the year?

   2007= 1 odd day=1%7=1

   2008= 2 odd days=3%7=3

   2009= 1 odd day=4%7=4

   2010=1 odd day=5%7=5

   2011= 1 odd day=6%7=6

   2012= 2 odd days=8%7=1 
   But 2012 is not a non leap year so the calendar will not be
   the same as 2007

   2013= 1 odd day=9%7=2

   2014=1 odd day=10%7=3

   2015= 1 odd day=11%7=4

   2016= 2 odd days=13%7=6

   2017= 1 odd day=14%7=0

  2018 is not leap year so the calendar will be the same as 2007.

9.  On what dates of May 2016 did Sunday fall?

    Consider 1^st may 2016

    1%7=1 odd day

    May=1 odd day

    2016=2000+15(3 leap years and 12 non leap years) =18%7
     =4 odd days

    So (1+1+4) %7=6 odd days

    Since May 2016 is after Feb 29^th we must add an odd day.
    So, 7 odd days i.e. (7%7=0) so Sunday.

    So 1^st, 8th, 15th, 22nd, 29th of May 2016 are Sundays

10.  What was the day of the week on 15^th august 1947?

     15%7=1 odd day

     August=2 odd days

     1947(1900+46) =1 odd day+ 11 leap years 
      and 35 non leap years
     = 58%7=2 odd days

     (1+2+2)%7=5 odd days, therefore Friday.

11.  The starting day of the leap year is Wednesday then 
what was the ending day of the same year?

      A leap year always ends with next day of the starting day 
      is Thursday.
     (366 days= 52 weeks and 2 odd days)

12.  What was the day of the week 12^th February 2020?

      12%7=5 odd days

      February=3 odd days

      2020(2000+19) = (15 non leap years and 4 leap years)
      =23 % 7=2 odd days

     (5+3+2)%7=3 odd days.
     So 12^th February 2020 is Wednesday.

13.  What was the day of the week 10^th June 2014?

     10%7=3 odd days

     June= 4 odd days

     2014(2000+13) = (13 non leap years and 3 leap years)
     =16%7= 2 odd days

     (3+4+2)%7 =2 odd days. So it is Tuesday.

14.  What was the day of the week 29^th February 2012?

       29%7=1 odd day

       Feb=3 odd days

       2012( 2000+12)=(11 non leap years  and 2 leap years)
        = 13 odd days

        But given date is 29 th feb 2012(leap year)= 1 odd day

        Total odd days=(1+3+13+1)%7=4 odd days

        So it is thursday

15.  What was the day of the week 2^nd March 2016?

      2%7=2 odd days

      March=3 odd days

      2016(2000+15) = (15 non leap years and 3 leap years) 
      = 18%7=4 odd days

     (2+3+4)%7=2 odd days. It is a leap year so an extra odd day 
      =3 odd days so it is Wednesday.