Total nines written from 1 to 1000

Question

Writing every integer from $1$ through $1000$ , how many times in total do you write the digit $9$ ? (A number like $919$ contributes two.)

Short answer

$300$ . Treat $0$ to $999$ as three-digit strings: each of the three positions shows $9$ in exactly $100$ of the $1000$ strings, giving $300$ . The numbers $0$ and $1000$ contain no $9$ s, so the answer is $300$ .

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Counting and Combinatorics

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