CEMC Cayley, 2009

Number theory Difficulty 2.0 Junior Find the answer Canada

How many integers $n$ are there with the property that the product of the digits of $n$ is 0, where $5000 \le n \le 6000$ ?

(A) $332$ (B) $270$ (C) $301$ (D) $272$ (E) $299$

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