Sum of digits - experience #23
Problem 294Published on Saturday, 29th May 2010, 09:00 am; Solved by 523; Difficulty rating: 45%
For a positive integer k, define d(k) as the sum of the digits of k in its usual decimal representation. Thus d(42) = 4+2 = 6.
For a positive integer n, define S(n) as the number of positive integers k < 10n with the following properties :
- k is divisible by 23 and
- d(k) = 23.
Find S(1112) and give your answer mod 109.