Question 4
For each positive integer $n$ let $f(n)$ be the value of the base-ten numeral $n$ viewed in base $b,$ where $b$ is the least integer greater than the greatest digit in $n.$ For example, if $n = 72,$ then $b = 8,$ and $72$ as a numeral in base $8$ equals $7 \cdot 8 + 2 = 58;$ therefore $f(72) = 58.$ Find the number of positive integers $n$ less than $1000$ such that $f(n) = n.$