An apartment block has a number of square apartments and a number of square gardens. Apartments must have at least one window, either to the out side or to a garden. In figure 1, one apartment has a window to an internal garden G, and ten have windows to the outside.

What is the smallest number of gardens needed for an apartment block built on a 6 x 6 square, as in figure 2, so that each apartment has a window to the outside or to an internal garden ?