Counting nines to 1000

How many times does the digit 99 appear when writing out all the integers from 11 to 10001000? (For instance, 919919 contributes two 99s.)

Show hints (2)+
  1. Pad to 33 digits (000000–999999): each digit appears 100100 times in each of the 33 positions.
  2. So 99 appears 3×1003\times100; 10001000 adds none.

Answer

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300

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