Evaluate this sum:

S(1) + S(2) +....+ S(2014), given that S(N) is the sum of the digits of N .

S(0) + S(1999) = 0 + 28 = 28

S(1) + S(1998) = 1 + 27 = 28

S(2) + S(1997) = 2 + 26 = 28

...

S(10) + S(1989) = 1 + 27 = 28

S(11) + S(1988) = 2 + 26 = 28

...

S(100) + S(1899) = 1 + 27 = 28

...

S(999) + S(1000) = 27 + 1 = 28

The sum of S(N) from N = 1 to 1999 = 28 * 1000 = 28000.  Then just add in 90 for the N from 2000 to 2014. 

Posted by tomarken on 2014-06-04 09:31:53