Practice Questions:
Question 1:
What was the day on September 22, 1973?
22nd September 1973 = 1972 years + (Jan 1, 1973 to Sep 22, 1973)
Odd Days:
1600 = 0 Odd Days
300 Years = 1 Odd Day
72 Years = 18 Leap Years + 54 Ordinary Years
= (18 * 2) + (54 * 1) = 90 days = 12 weeks + 6 day = 6 Odd Days
So, 0+1+6 = 7 = 0 Odd Days till 1972.
For 1973, counting days from Jan to Sep,
31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 22 = 265 days = 37 weeks + 6 days = 6 Odd Days
So, 0 + 6 = 6 Odd Days
As Odd day 6 corresponds to Saturday, 22nd September, 1973 is SATURDAY.
Odd Days:
1600 = 0 Odd Days
300 Years = 1 Odd Day
72 Years = 18 Leap Years + 54 Ordinary Years
= (18 * 2) + (54 * 1) = 90 days = 12 weeks + 6 day = 6 Odd Days
So, 0+1+6 = 7 = 0 Odd Days till 1972.
For 1973, counting days from Jan to Sep,
31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 22 = 265 days = 37 weeks + 6 days = 6 Odd Days
So, 0 + 6 = 6 Odd Days
As Odd day 6 corresponds to Saturday, 22nd September, 1973 is SATURDAY.
Question 2:
The Last day of the century cannot be?
100 years = 5 Odd Days. So, last day of the 1st century is Friday.
200 years = 10 = 3 Odd Days. So, the last day of the 2nd century is Wednesday.
300 years = 15 = 1 Odd Day. So, the last day of the 3rd century is Monday.
400 years = 20 + 1 = 21 = 0 Odd Days. So, the last day of the 4th century is Sunday.
The same cycle of Friday, Wednesday, Monday and Sunday gets repeated.
Hence, the last day of the century cannot be a TUESDAY or a THURSDAY or a SATURDAY.
Question 3:
On what dates of April 2001, did Sunday fall?
Let's find the day of April 1, 2001.
2000 = 0 Odd Days
For 2001, counting days from Jan to April,
31 + 28 + 31 + 1 = 91 days = 13 weeks = 0 Odd Days
So, 0 + 0 = 0 Odd Days = Sunday.
Hence, 1st Sunday in April 2001 was April1.
Other Sundays were 8, 15, 22, 29.
Thus, April 1, April 8, April 15, April 22 and April 29 of 2001 were Sundays.
Question 4:
The Calendar for the year 2005 is the same for the year?
Counting the number of days from 2005 onwards to get 0 Odd Day,
2005 + 2006 + 2007 + 2008 + 2009 + 2010 + 2011 = 1 + 1 + 1 + 2 + 1 + 1 = 7 = 0 Odd Days
Therefore, the calendar of 2011 is same as the year of 2005.
Counting the number of days from 2005 onwards to get 0 Odd Day,
2005 + 2006 + 2007 + 2008 + 2009 + 2010 + 2011 = 1 + 1 + 1 + 2 + 1 + 1 = 7 = 0 Odd Days
Therefore, the calendar of 2011 is same as the year of 2005.
Question 5:
Today Friday, after 62 days, it will be?
Each day of the week is repeated after 7 days. So, after 63 days, it will be Friday.
Hence, after 62 days, it will be a THURSDAY.
Time to Think:
What will be the day on October 15, 2020?
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