# Product Digit Not Zero

**Number Theory**Level 3

Define \( p(n) \) to be the product of all (decimal) digits of the number \(n\).

What is the value of

\[ p(1) + p(2) + p(3) + p(4) + \ldots + p(999)? \]

Do not include leading zeros in the product.

Define \( p(n) \) to be the product of all (decimal) digits of the number \(n\).

What is the value of

\[ p(1) + p(2) + p(3) + p(4) + \ldots + p(999)? \]

Do not include leading zeros in the product.

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