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Found problems: 1

2017 Israel National Olympiad, 2
Tags: number theory , product , digit , maximize
Denote by $P(n)$ the product of the digits of a positive integer $n$. For example, $P(1948)=1\cdot9\cdot4\cdot8=288$. [list=a] [*] Evaluate the sum $P(1)+P(2)+\dots+P(2017)$. [*] Determine the maximum value of $\frac{P(n)}{n}$ where $2017\leq n\leq5777$. [/list]