Which year has the same calendar as that of 2009?

The correct option is 2015.

To determine which year has the same calendar as 2009, we need to find a year such that the number of odd days between 2009 and that year is a multiple of 7 (i.e., 0 odd days in total). Additionally, both years must be of the same type (either both ordinary years or both leap years) so that the calendar matches exactly.

An ordinary year (365 days) has 1 odd day (since 365 divided by 7 leaves a remainder of 1).
A leap year (366 days) has 2 odd days (since 366 divided by 7 leaves a remainder of 2).

Let's count the odd days starting from the year 2009 onwards:

2009 (Ordinary year) = 1 odd day
2010 (Ordinary year) = 1 odd day
2011 (Ordinary year) = 1 odd day
2012 (Leap year) = 2 odd days
2013 (Ordinary year) = 1 odd day
2014 (Ordinary year) = 1 odd day

Now, let's sum the odd days from 2009 up to the end of 2014 (which is just before 2015 starts):
Total odd days = 1 (for 2009) + 1 (for 2010) + 1 (for 2011) + 2 (for 2012) + 1 (for 2013) + 1 (for 2014) = 7 odd days.

Since the sum of the odd days is 7 (which is a multiple of 7, leaving a remainder of 0), the calendar will repeat in the next year, which is 2015.

Since 2009 is an ordinary year and 2015 is also an ordinary year, their calendars will be identical.