KöMaL 2012 C1110

Andrew is going for a walk, starting from a corner of a block in a housing estate where streets form a rectangular lattice. During his walk, he only changes direction at street corners. The buildings form square blocks, 15 m on a side, and the width of the streets is negligible. Show that if Andrew ends his walk at the starting point, then the length of his path in metres will be an even number.