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 Sum Month and Day (Posted on 2010-01-14)
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).

 No Solution Yet Submitted by K Sengupta Rating: 1.0000 (1 votes)

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 possible solution | Comment 2 of 5 |
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 sum-days.  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 sum-days.

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 2010-01-14 18:02:32

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