  In combinatorics on words, a word $w$ over an alphabet $\Sigma$ is said to
avoid a pattern $p$ over an alphabet $\Delta$ 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 $p$. A pattern is said to be doubled if no
variable occurs only once. Doubled patterns with at most 3 variables and
patterns with at least 6 variables are $3$-avoidable. We show that doubled
patterns with 4 and 5 variables are also $3$-avoidable.
