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Sum Settlement (Posted on 2014-06-03) Difficulty: 3 of 5
Evaluate this sum:

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

No Solution Yet Submitted by K Sengupta    
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Solution solution | Comment 3 of 4 |


Consider the set of all integers from 0 to 99 written as a 3-digit numbers, i.e. adding leading zeroes to numbers below 100.
 
We get 10^3 triplets with all decimal digits equally appearing, averaging 4.5 .
Thus a sum of 3000*4.5 = 13500 is reached.

In the next thousand each triplet is prefixed by a digit 1, rending the accrued sum  of 14500.


Add 90 (accounting for 2000-2014) to reach
the final result:13,500+14,500+90 = 28090.



  Posted by Ady TZIDON on 2014-06-04 02:13:57
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