In the diagram, a shaded rectangle is drawn on each of four faces
of a cube to form a band around the cube.
Which of the following could not be the net of the cube?
(A) (B) [[IMAGE1]] (C) [[IMAGE2]] (D) [[IMAGE3]] (E) [[IMAGE4]]
Problem 116
Official solution
The net shown in (B) could not be the net of the cube.
Using the net in (B), we begin by labelling three squares "bottom", "O"
and "P", as shown.
[[IMAGE0]]
We then fold the net so that the face labelled bottom is the bottom
face of the cube, and the two faces labelled O and P, folded upward,
become two adjacent vertical faces of the cube.
The bottom of the cube, along with the two folded vertical faces are
shown in the second diagram.
[[IMAGE1]]
We ignore the other three faces of the cube, since the faces labelled
O and P are sufficient for demonstrating that the net in (B) cannot be
folded to give the required band around the cube.