Question

What will be the day of the week on 1st January, 2010?

Answer 1

Hint: In a year, there are $52$ weeks and each week consists of 7 days. Using this, we observe that there is 1 odd day in a non-leap year and 2 odd days in a leap year. We shall calculate the number of odd days from $2000$ to $2010$ and then find the day of the week.

Complete step-by-step answer:
We know that there are $52$ weeks in a year and each week consists of 7 days. We also know that there are $365$ days in a year. But $52$ weeks gives $52 \times 7 = 364$ days.
So, a non-leap year has 1 odd day. In a leap year, there are $366$ days. So, a leap year has 2 odd days.
Since 2000 was a leap year, number of odd days in $2000 = 2$
2001 was a non-leap year. So, the number of odd days in $2001 = 1$
2002 was a non-leap year. Number of odd days in $2002 = 1$
2003 was a non-leap year. Number of odd days in $2003 = 1$
2004 was a leap year. The number of odd days in $2004 = 2$
2005 was a non-leap year. The number of odd days in $2005 = 1$
2006 was a non-leap year. Number of odd days in $2006 = 1$
2007 was a non-leap year. Number of odd days in $2007 = 1$
2008 was a leap year. The number of odd days in $2008 = 2$
2009 was a non-leap year. Number of odd days in $2009 = 1$
Now, 2010 is also a non-leap year. So, the number of odd days in $2010 = 1$.
Total number of odd days from 2000 to 2010 $= 2 + 1 + 1 + 1 + 2 + 1 + 1 + 1 + 2 + 1 + 1 = 14$
We know that 7 odd days make a week. So, 14 days will make up 2 weeks. Hence,
Number of odd days from $2000{\text{ to }}2010 = 0$.
Thus, the day of the week on 1st January, 2010 will be a Sunday.

Note: Leap occurs after every four year, so to find whether a given year is a leap year or a non-leap year, it should be divided by 4. If the given year is completely divisible by 4, then it is a leap year, otherwise, it is a non-leap year. In the non-leap year February has 28 days but in leap year it has 29 days.