perplexus.info :: General : Sum Month and Day

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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