data/problems/294.yml
---
:id: 294
:name: 'Sum of digits - experience #23'
:url: https://projecteuler.net/problem=294
:content: |+
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 \< 10<sup>n</sup> 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(11<sup>12</sup>) and give your answer mod 10<sup>9</sup>.