MathDB

Let

n\in \mathbb{Z}_{> 0}

. The set

S

contains all positive integers written in decimal form that simultaneously satisfy the following conditions: [*] each element of

S

has exactly

n

digits; [*] each element of

S

is divisible by

3

; [*] each element of

S

has all its digits from the set

\{3,5,7,9\}

Find

\mid S\mid

Problem Statement