This is the dumbest problem ever!!! who would assume that matches don't perfectly fit together??? That means you also need to assume that match heads stick out further than the stick so you will never get a straight line, and thus will never make a square. If you assume that, then NONE of your matchstick problems can be solved.
if we move a vertical stick next to fly's head and a horizontal one just up of the fly. then we also get a square.