It is observed that January 1, 2002 was the first "sumday" of the 21st century, that is, when that date is written in the mmddyy format, it becomes 01/01/02, and 1+1 = 2. More specifically, a "sumday" is a date in which the month and the day add up to the year.
(i) Determine the total number of sumdays from January 1, 2002 to December 31, 2100 inclusively.
(ii) Determine the last sumday in the period covered under (i).
EDIT: My tallies below were correct, I just put the wrong number It should have been 365.
With the help of a spreadsheet program, I tallied 365 sumdays. With 12/31/43 as the last sum day.
Here are my sum days for each month/day combo, the tallies, being the last combo with the year. 01/01/02, 01/02/03, 01/03/04...01/31/32 January's tally is thus 31 sumdays.
Jan  31
Feb  28
Mar  31
Apr  30
May  31
Jun  30
Jul  31
Aug  31
Sept  30
Oct  31
Nov  30
Dec 31, with 12/31/43 being the last possible sum day, no leap years need to be considered since 2 + 29 = 31, which will not exist.
Edited on January 19, 2010, 4:47 pm

Posted by Cyriis
on 20100114 18:02:32 