# IMO training problem

Logic Level 3

Given a positive integer $$n$$, let $$p(n)$$ be the product of the non-zero digits of $$n$$. (If $$n$$ has one digit, then $$p(n)$$ is equal to that digit.) Let

$S = p(1) + p(2) + \cdots + p(999).$

What is the largest prime factor of $$S$$?

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