×If you checkerboard-colour the trapdoors, because of the orthogonal tiles, you can only move from one colour to the other, so you can use a parity argument to determine what colour you must start on. In the case of this puzzle, that eliminates all but two start points.

One of the two is the middle tile on the lower-right, and this can be ruled out because whichever side you move to, the trapdoor on the other side becomes a dead end.