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).

(i) There are 2487 sum digit-days from January 1, 2002 to December 31, 2099 inclusively.
Only 1 year need special observation for the leap day which has a sum digit-day value of [0+2 + 2+9 =] 13 . That leap year is 2076 [7+6 = 13]. 

(ii) The years -- 2019, 2028, 2029, 2037, 2038, 2046, 2047, 2055, 2056, 2064, 2065, 2073, 2074, 2082, 2083, 2091, and 2092 -- each have 36 sum-days. [The sum digit values of these years are 10 and 11].

(iii) September 27, 2099 [9/27/99] is the final sum digit-day of the 21st century.

Posted by Dej Mar on 2011-09-20 13:33:13