Overhang

How far off the edge of the table can we reach by stacking $n$ identical, homogeneous, frictionless blocks of length 1? A classical solution achieves an overhang of $1\mathrm{/}2H_n$, where $H_n\ln n$ is the $n$th harmonic number. This solution is widely believed to be optimal. We show, however, that it is, in fact, exponentially far from optimality by constructing simple $n$-block stacks that achieve an overhang of $c{n}^{1\mathrm{/}3}$, for some constant $c>0$.