Grid walking with poison

Discrete Mathematics Level pending

An ant is in a corner (the upper-left red point in the picture) of a tiled room and she wants to get to the diagonally opposite corner (bottom-right red point in the picture). The ant can only move along the lines between the tiles (the borders); at each step she always reduces her distance to the destination. But, she can´t touch a small square area of 2 x 2 tiles where a mortal poison lies.

Find the number of paths the ant can safely follow without touching the poisoned tiles. The ant will be poisoned if she touches any of the four sides of one poisoned tile.

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