Integers that contain a zero

How many of the positive integers from 11 to 1000010000 (inclusive) contain the digit 00 at least once?

Show hints (2)+
  1. Count the complement: numbers with no zero digit, grouped by number of digits (each digit 1199).
  2. Subtract from 99999999, then remember to handle 1000010000 separately.

Answer

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2620

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Asked at: Jane Street, Citadel

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