quarantine 'em

...which rules out the obvious solution with nine trolls arranged in a square grid pattern, five spaces apart, one at the centre

I've found that placing trolls adjacent to one another doesn't generally allow them to threaten more territory than spreading them apart...

...except for a L-shaped arrangement of three, which threatens a region not possible with any three separate trolls.

(Of course, in the "real" game, bunching together is more useful than in this problem.)

Note that it isn't necessary to for the trolls threaten the *entire* board (which I don't think is possible even with nine of them)...

Since the lone dwarf *must* move, it suffices to threaten the whole board except for one square...

Or, better yet, to threaten the entire board except for a network of squares, no two of which are connected by a dwarf's move.

The fact that a troll, too, must be moved may complicate the actual procedure of assembling this trap.