We are given a cube with edges of length n cm. At our disposal is a long piece of insulating tape of width 1 cm. It is required to stick this tape to the cube. The tape may freely cross an edge of the cube on to a different face but it must always be parallel to an edge of the cube. It may not overhang the edge of a face or cross over a vertex. How many pieces of the tape are necessary in order to completely cover the cube? (You may assume that n is an integer.) (A Spivak) geometry3D geometrycombinatoricscombinatorial geometry