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 the cubes shown in Panel II, which one of the options is correct?
(Panel I shows a flat cross-shaped net of six squares: a vertical strip of four squares one above another, with one extra square attached to the left of the second square in that strip and another extra square attached to its right, all joined along dashed fold lines. Some squares carry grey shaded regions and some are left plain white. Panel II shows two separate solid cubes, labelled (i) and (ii), each with grey shaded regions on some of their visible faces.)

Question

Coloured strips are printed on a transparent sheet as shown below. The bottom half of this sheet is folded backwards along the PQ axis to form a semi-circle. Which of the option(s) will be a part of the resultant semi-circle?

Answer 1

A quick way to check a cube-folding question like this is to pick two shaded faces that share an edge in the flat net, and then check every candidate cube to see if those same two faces still share an edge in the same relative direction after folding. If the shared edge or the rotation does not match, that candidate is impossible, no matter how correct it looks at first glance.

In the net, the square carrying the grey diagonal triangle sits right next to the square carrying the small grey corner patch, joined along one fold line, and the fully grey square sits at the far end of the strip, which becomes the face directly opposite the front face once folded. The mostly grey square with the white notch sits on the opposite side of the strip from the small-patch square, so it becomes the left face while the small-patch square becomes the right face.

Cube (i): The shaded faces visible on this cube do not sit next to each other the way the net demands. Folding a flat net fixes both which faces touch and how their patterns line up along that shared edge, and cube (i) breaks this requirement, so it cannot be the result of folding Panel I.
Cube (ii): The shaded faces visible on this cube touch each other along the same edge, and in the same rotation, that the net produces when folded. Every shaded region lands on the correct face in the correct orientation, so cube (ii) is a valid folded form of Panel I.

Since cube (i) fails the adjacency and orientation check while cube (ii) passes it, only cube (ii) can be the actual folded cube.

Let's summarize:

Folding a net fixes not just which face goes where, but also how each face is rotated relative to its neighbors.
Two shaded faces that are neighbors in the flat net must stay neighbors, in the same relative rotation, after folding.
Cube (i) violates this, cube (ii) satisfies it, so only (ii) is a valid fold of the net in Panel I.

So the correct choice is that only (ii) can correspond to the unfolded cube in Panel I, which is option (B).

Answer 2

A quick way to check a cube-folding question like this is to pick two shaded faces that share an edge in the flat net, and then check every candidate cube to see if those same two faces still share an edge in the same relative direction after folding. If the shared edge or the rotation does not match, that candidate is impossible, no matter how correct it looks at first glance.

In the net, the square carrying the grey diagonal triangle sits right next to the square carrying the small grey corner patch, joined along one fold line, and the fully grey square sits at the far end of the strip, which becomes the face directly opposite the front face once folded. The mostly grey square with the white notch sits on the opposite side of the strip from the small-patch square, so it becomes the left face while the small-patch square becomes the right face.

Cube (i): The shaded faces visible on this cube do not sit next to each other the way the net demands. Folding a flat net fixes both which faces touch and how their patterns line up along that shared edge, and cube (i) breaks this requirement, so it cannot be the result of folding Panel I.
Cube (ii): The shaded faces visible on this cube touch each other along the same edge, and in the same rotation, that the net produces when folded. Every shaded region lands on the correct face in the correct orientation, so cube (ii) is a valid folded form of Panel I.

Since cube (i) fails the adjacency and orientation check while cube (ii) passes it, only cube (ii) can be the actual folded cube.

Let's summarize:

Folding a net fixes not just which face goes where, but also how each face is rotated relative to its neighbors.
Two shaded faces that are neighbors in the flat net must stay neighbors, in the same relative rotation, after folding.
Cube (i) violates this, cube (ii) satisfies it, so only (ii) is a valid fold of the net in Panel I.

So the correct choice is that only (ii) can correspond to the unfolded cube in Panel I, which is option (B).

Show Hint

The Correct Option is B

Solution and Explanation

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