Problem 294

Sum of digits - experience #23

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 n with the following properties :

- k is divisible by 23 and
- d(k) = 23.

Find S(11^{12}) and give your answer mod 10^{9}.

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