A "sum digit-day" is a date in which the sum of the digits of the month and the day add up to the sum of the digits of the year in the mm-dd-yy format.

For example,12-18-84 is a sum digit-day as the respective sum of the digits of the month and the day add up to 12 which is equal to the sum of the digits of the year.

(i) Determine the total number of sum digit-days from January 1, 2002 to December 31, 2099 inclusively.

(ii) Determine the year(s) having the maximum number of sum digit- days in the period covered under (i).

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

Part 1 is way too much work.  I wouldn't attempt it without a computer program.  Even the year 2004 had at least 17 days and the chances are I missed one.

Part 2 is probably the year 2099 since a sum of 18 can be reached in many ways.  Or it may be 2093 since a sum of 12 can be achieved at the end of Oct, Nov, & Dec.  Again, I don't want to try counting them all.

Part 3 would be 9-27-99

Edited on September 21, 2011, 8:57 am

Posted by Jer on 2011-09-20 11:26:47