A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?
Show Hint
Use the shaded diamond face as a fixed reference point, then check whether the neighboring faces' shading lands in the same rotational position (never mirrored) as a genuine fold of the net would produce.
Only (i) can correspond to the unfolded cube in Panel I.
Only (ii) can correspond to the unfolded cube in Panel I.
Both (i) and (ii) can correspond to the unfolded cube in Panel I.
Neither (i) nor (ii) can correspond to the unfolded cube in Panel I.
Show Solution
The Correct Option isA
Solution and Explanation
Step 1: Work out which pairs of net faces become opposite faces of the cube. A different way to attack this kind of folding question is to first sort the six faces of the net into three opposite pairs, instead of tracking adjacency directly. When a strip of four squares in a row is rolled into a tube to form four side faces of a cube, any two squares that are two positions apart in that strip end up directly opposite each other, while squares next to each other in the strip end up as adjacent side faces. The two extra flap squares attached at the ends of the strip fold over to become the remaining top and bottom faces, each ending up opposite the other flap and adjacent to the strip faces nearest to where it was attached.
Step 2: Apply this to the diamond face. Using this pairing, the diamond square is opposite one specific face of the net (the one two positions away from it in the strip) and adjacent to the two faces on either side of it in the strip, plus whichever flap face folds up next to it. Only faces that are genuinely adjacent to the diamond square in the net can end up visible next to the diamond face on a folded cube, since opposite faces of a cube can never be seen together in a single view.
Step 3: Eliminate any option that pairs the diamond with a face that should be opposite it. If either candidate cube in Panel II showed the diamond face next to a face that the net actually makes opposite to it, that candidate could be rejected immediately, since two opposite faces can never appear side by side in the same 3D view. Checking both cubes shows this is not the issue here, both (i) and (ii) pair the diamond only with genuinely adjacent net faces; the difference between them lies purely in how those adjacent faces are rotated.
Step 4: Settle the remaining cube using rotation, not adjacency. Since both candidates pass the adjacency test, compare the exact rotational placement of the triangular shading on the faces next to the diamond. Physically folding the net can only rotate each face's pattern about its hinge line, never flip it into a mirror image. Cube (i) shows the triangular shading in the position that this rotation actually produces, while cube (ii) shows it in the mirrored position, which folding cannot create.
Final Answer: Only cube (i) matches a genuine fold of the net in Panel I, so option (A) is correct.
