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Sum of digits - experience #23

Problem 294

Published on 29 May 2010 at 09:00 am [Server Time]

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.


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