for my $pos (keys %map) {
   add_solutions($pos, $dict);
}

my %seen;
sub add_solutions {
    my ($node, $tree) = @_;

    local $seen{$node} = 1;
    my $char = $board{$node};
    $tree = $tree->{$char} or return;

    push @solutions, $tree->{word} if $tree->{word};

    for my $new_node (grep not $seen{$_}, @{$map{$node}}) {
        add_solutions($new_node, $tree);
    }
}