Can you find the digit?

Computer Science Level 2

\[ S=123456789101112131415161718192021\ldots \]

Given that the string \(S\) is the concatenation of the first 1,000,000,000 positive integers in ascending order, find the \(999999999^{\text{th}}\) digit of \(S\).

Details and Assumptions:

By the \(x^{\text{th}}\) digit of \(S\), we mean the digit in the \(x^{\text{th}}\) place from the left in the decimal representation of \(S\).

Some explicit examples are :

  • The \(5^{\text{th}}\) digit of the number \(14583469\) is \(3\).
  • The \(4^{\text{th}}\) digit of the number \(143256\) is \(2\).

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