Each of the pieces has from 1 to 6 points. When the puzzle is assembled 26 of those points are on the outside edge and 14 points are in the interior. When the 13 individual pieces are examined and we could the points on them the total comes to 40. It turns out that if any piece is put in a location with an orientation that does not have the maximum possible points on the outside edge that it will not be possible to find a solution. To find a solution just start out putting pieces around the outside of the outline with as many points on the outside edge as possible.
Click here are some placements that will make it impossible to be part of a solution.