Choose the box that is similar to the box formed from the given sheet of paper…

Concept: When a flat net is folded into a cube, the opposite faces can be read off the net's layout. In a straight strip of four squares (a row or column of four), the 1st and 3rd squares become opposite faces, and the 2nd and 4th squares become opposite faces. A square attached to the side of that strip pairs up with the other side-attached square to form the remaining opposite pair. Two faces that are opposite on a cube can never be seen together, adjacent to one another, in any 3-face corner view of the assembled cube.

Application:

1. In sheet (X), the squares form a vertical strip F-E-B-C from top to bottom, so by the rule above F is opposite B (1st and 3rd), and E is opposite C (2nd and 4th).

2. A is attached to the left side of E, and D is attached to the right side of C; these are the two remaining faces, so A and D are opposite each other.

3. So the three opposite pairs for this cube are: F ↔ B, E ↔ C, A ↔ D.

Cross-check: test each candidate cube against these opposite pairs — a candidate is impossible the moment it shows two opposite faces together.

• Cube (1) shows F, B and E together — F and B are an opposite pair, so this cube is impossible.

• Cube (3) shows E, B and C together — E and C are an opposite pair, so this cube is impossible.

• Cube (4) shows D, E and A together — A and D are an opposite pair, so this cube is impossible.

• Cube (2) shows F, E and D together — none of F-E, E-D or F-D is an opposite pair, so these three faces can genuinely meet at one corner of the cube.

Hence only the cube in figure (2) can be formed from sheet (X); the correct choice is ‘2 only’.