MathNet 2016-part-07 — 182 problems (EN–VI) Question 158

A nonempty set $S$ is called well-filled if for every $m \in S$, there are fewer than $\frac{1}{2} m$ elements of $S$ which are less than $m$. Determine the number of well-filled subsets of $\{1,2, \ldots, 42\}$.