It is observed that January 1, 2002 was the first "sum-day" of the 21st century, that is, when that date is written in the mm-dd-yy format, it becomes 01/01/02, and 1+1 = 2. More specifically, a "sum-day" is a date in which the month and the day add up to the year.

(i) Determine the total number of sum-days from January 1, 2002 to December 31, 2100 inclusively.

(ii) Determine the last sum-day in the period covered under (i).

Every usual date of the year will be a sum-day exactly once. 
The unusual date being February 29.  It would be a sum-day in 2031 which is not a leap year.

So the answer is 365 sum-days.

The last is the highest sum 12/31/43.

Posted by Jer on 2010-01-14 14:58:35