Integers up to ten thousand containing a zero

Question

Among the integers $1,2,\dots,10000$ , how many contain at least one digit $0$ ?

Short answer

$2620$ . Count the zero-free ones instead: $9+9^2+9^3+9^4=7380$ numbers with one to four digits, and $10000$ itself contains zeros. So $10000-7380=2620$ .

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Lessons behind this question

Counting and Combinatorics

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