The calendar for the year 2009 will be the same as that of the year

### Concept & Calendar Repetition Cycle A calendar year repeats when the cumulative sum of odd days from the starting year becomes exactly divisible by 7, and the resulting matching year is of the exact same type (ordinary or leap). ### Step-by-Step Solution - Let's count the odd days starting from 2009. - 2009 (ordinary) = 1 odd day - 2010 (ordinary) = 1 odd day - 2011 (ordinary) = 1 odd day - 2012 (leap) = 2 odd days - 2013 (ordinary) = 1 odd day - 2014 (ordinary) = 1 odd day - Sum of odd days from 2009 to 2014 = $1 + 1 + 1 + 2 + 1 + 1 = 7$. - Since $7 \pmod 7 = 0$, the year immediately following 2014 will have the identical calendar. - The next year is 2015. - Verify year type: Both 2009 and 2015 are ordinary years, so the entire calendar matches perfectly. ### Exam Strategy & Shortcut Determine how many years the target year is past the previous leap year. 2009 is 1 year after a leap year (2008). Ordinary years that immediately follow a leap year ALWAYS repeat after exactly 6 years. $2009 + 6 = 2015$. ### Common Pitfall Assuming all calendars repeat every 11 years. Only ordinary years that are 2 or 3 years past a leap year repeat in 11 years. Ordinary years 1 year past a leap year repeat in 6 years. ### Final Answer Therefore, the correct answer is **2015**.