  I. J. Good (1941) showed that the set of irrational numbers in $(0,1)$ whose
partial quotients $a_n$ tend to infinity is of Hausdorff dimension $1/2$. A
number of related results impose restrictions of the type $a_n\in B$ or
$a_n\geq f(n)$, where $B$ is an infinite subset of $\mathbb N$ and $f$ is a
rapidly growing function with $n$. We show that, for an arbitrary $B$ and an
arbitrary $f$ with values in $[\min B,\infty)$ and tending to infinity, the set
of irrational numbers in $(0,1)$ such that \[ a_n\in B,\ a_n\leq f(n)\text{ for
all $n\in\mathbb N$, and }a_n\to\infty\text{ as }n\to\infty\] is of Hausdorff
dimension $\tau(B)/2,$ where $\tau(B)$ is the exponent of convergence of $B$.
