A) What is the last sum-day of the 21st century? B) How many sum-days are there in the 21st century?

Some people believe that January1,2000 is the first day of the21st century. Other people believe that the honor belongs to January1,2001. But everyone should agree that January1,2002 is the first "sum-day" of the new century- when you write out that date in standard notation, it becomes01/01/02, and1+1=2. More generally, a sum-day is a date in which the day and month add up to the year.