  A word is said to be \emph{bordered} if it contains a non-empty proper prefix
that is also a suffix. We can naturally extend this definition to pairs of
non-empty words. A pair of words $(u,v)$ is said to be \emph{mutually bordered}
if there exists a word that is a non-empty proper prefix of $u$ and suffix of
$v$, and there exists a word that is a non-empty proper suffix of $u$ and
prefix of $v$. In other words, $(u,v)$ is mutually bordered if $u$ overlaps $v$
and $v$ overlaps $u$. We give a recurrence for the number of mutually bordered
pairs of words. Furthermore, we show that, asymptotically, there are $c\cdot
k^{2n}$ mutually bordered words of length-$n$ over a $k$-letter alphabet, where
$c$ is a constant. Finally, we show that the expected shortest overlap between
pairs of words is bounded above by a constant.
