## Sum of digits - experience #23

### Problem 294

Published on Saturday, 29th May 2010, 09:00 am; Solved by 508

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.

You are given that S(9) = 263626 and S(42) = 6377168878570056.

Find S(1112) and give your answer mod 109.