  The Snake-in-the-Box problem is that of finding a longest induced path in an
$n$-dimensional hypercube. We prove new lower bounds for the values $n\in
\{11,12,13\}$. The Coil-in-the-Box problem is that of finding a longest induced
cycle in an $n$-dimensional hypercube. We prove new lower bounds for the values
$n\in \{12,13\}$.
