For *non-negative integers* $a_1, a_2, a_3, \ldots , a_n \leq 9$, let

$f(a_1, a_2, \ldots , a_n) = a_1 + 11a_2 + 111a_3 + \ldots + \underbrace{111 \ldots 111}_{\text{Number of 1s}=n}a_n$

Find number of *positive integers* $N \lt 10^7$ such that there exists ** no** possible set of

All of my problems are **original**.