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?

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 second, complementary way to check this kind of question is to first work out which pairs of squares in the net become opposite faces of the cube (faces that can never be seen together in a single 2D picture of the cube), and then use that to rule out impossible pictures before even worrying about exact shading direction.

Map out the net: in a net made of a straight run of four squares plus one square attached on each side near the two ends, the two squares that are not in the straight run of four end up opposite each other once folded, and, within the run of four, the 1st and 3rd squares become opposite each other, and the 2nd and 4th squares become opposite each other.
Locate the diamond and triangle squares: using this rule on Panel I, the diamond square and the shaded triangle square that appear together as neighbors in cube (i) and (ii) are genuinely adjacent in the net, not opposite, so both can legally show up together on a single 2D cube drawing. This rules out rejecting either cube purely on adjacency grounds.
Decide the remaining check with orientation: since both faces are legally adjacent, the only thing left to test is whether the triangle's shaded corner sits on the correct side of the shared edge with the diamond. Physically folding the net, without flipping it over, fixes this orientation uniquely, in the same sense it appears flat in Panel I.
Apply the orientation test: cube (i) preserves this fixed orientation between the diamond and the triangle, while cube (ii) shows the triangle shading as a mirror image of what a real fold would produce, something only possible if the sheet were turned over, which folding along a crease never does.

So adjacency alone does not settle the question, but the orientation of the shading across the shared edge does, and it rules out cube (ii) while confirming cube (i).

Let's summarize:

The diamond and triangle faces are adjacent in the net, so both cubes are geometrically possible at first glance.
Only the orientation of the shading across their shared edge, fixed by the actual fold, decides the answer.
Cube (i) keeps the correct orientation; cube (ii) shows a mirrored, impossible orientation.

Only cube (i) can be produced by folding the net in Panel I, so the answer is option (A).

Answer 2

A second, complementary way to check this kind of question is to first work out which pairs of squares in the net become opposite faces of the cube (faces that can never be seen together in a single 2D picture of the cube), and then use that to rule out impossible pictures before even worrying about exact shading direction.

Map out the net: in a net made of a straight run of four squares plus one square attached on each side near the two ends, the two squares that are not in the straight run of four end up opposite each other once folded, and, within the run of four, the 1st and 3rd squares become opposite each other, and the 2nd and 4th squares become opposite each other.
Locate the diamond and triangle squares: using this rule on Panel I, the diamond square and the shaded triangle square that appear together as neighbors in cube (i) and (ii) are genuinely adjacent in the net, not opposite, so both can legally show up together on a single 2D cube drawing. This rules out rejecting either cube purely on adjacency grounds.
Decide the remaining check with orientation: since both faces are legally adjacent, the only thing left to test is whether the triangle's shaded corner sits on the correct side of the shared edge with the diamond. Physically folding the net, without flipping it over, fixes this orientation uniquely, in the same sense it appears flat in Panel I.
Apply the orientation test: cube (i) preserves this fixed orientation between the diamond and the triangle, while cube (ii) shows the triangle shading as a mirror image of what a real fold would produce, something only possible if the sheet were turned over, which folding along a crease never does.

So adjacency alone does not settle the question, but the orientation of the shading across the shared edge does, and it rules out cube (ii) while confirming cube (i).

Let's summarize:

The diamond and triangle faces are adjacent in the net, so both cubes are geometrically possible at first glance.
Only the orientation of the shading across their shared edge, fixed by the actual fold, decides the answer.
Cube (i) keeps the correct orientation; cube (ii) shows a mirrored, impossible orientation.

Only cube (i) can be produced by folding the net in Panel I, so the answer is option (A).

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

The Correct Option is A

Solution and Explanation

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