  In combinatorics on words, a word $w$ over an alphabet $\Sigma$ is said to
avoid a pattern $p$ over an alphabet $\Delta$ of variables if there is no
factor $f$ of $w$ such that $f=h(p)$ where $h:\Delta^*\to\Sigma^*$ is a
non-erasing morphism. A pattern $p$ is said to be $k$-avoidable if there exists
an infinite word over a $k$-letter alphabet that avoids $p$. We consider the
patterns such that at most two variables appear at least twice, or
equivalently, the formulas with at most two variables. For each such formula,
we determine whether it is $2$-avoidable, and if it is $2$-avoidable, we
determine whether it is avoided by exponentially many binary words.
