Explanation

Identify the type of each year:

2009: Ordinary year (365 days) 2010: Ordinary year (365 days) 2011: Ordinary year (365 days) 2012: Leap year (366 days) 2013: Ordinary year (365 days) 2014: Ordinary year (365 days) 2015: Ordinary year (365 days) 2016: Leap year (366 days) 2017: Ordinary year (365 days) 2018: Ordinary year (365 days) Calculate the cumulative odd days from 2009 to each subsequent year:

2010: 1 odd day (2009) 2011: $1$ (2009) + $1$ (2010) = $2$ odd days 2012: $2$ (from previous) + $1$ (2011) = $3$ odd days 2013: $3$ (from previous) + $2$ (2012) = $5$ odd days 2014: $5$ (from previous) + $1$ (2013) = $6$ odd days 2015: $6$ (from previous) + $1$ (2014) = $7$ odd days = $0$ odd days (since 7 is a multiple of 7) 2016: $0$ (from previous) + $1$ (2015) = $1$ odd day 2017: $1$ (from previous) + $2$ (2016) = $3$ odd days 2018: $3$ (from previous) + $1$ (2017) = $4$ odd days

Since the cumulative odd days from 2009 to 2015 total 7 (a multiple of 7), 2015 has 0 odd days relative to 2009. This means 2015 shares the same calendar as 2009.