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

Concept: In a cube's net, when four squares form an unbroken straight line (a row or a column), the 1st and 3rd squares become an opposite-face pair once the net is folded, and the 2nd and 4th squares become another opposite-face pair. A face attached beside this straight run becomes adjacent, not opposite, to the face it touches in the net. Since a cube has exactly three opposite-face pairs, once two pairs are fixed the two faces left over must form the third pair. Also, any three faces that meet at one visible corner of a folded cube are always mutually adjacent, so they can never include two faces from the same opposite pair.

1. In sheet (X), the faces F, E, B, and C form an unbroken vertical straight line of four squares. By the straight-line rule, the 1st and 3rd faces are opposite, and the 2nd and 4th faces are opposite: so F is opposite B, and E is opposite C.

2. The two remaining faces, A (attached beside E) and D (attached beside C), are not part of either fixed pair. Since a cube has only three opposite pairs and two are already fixed, A and D must form the third pair: A is opposite D.

3. The sheet's three opposite pairs are therefore F-B, E-C, and A-D. A valid folded cube can never show two faces from the same pair meeting at one corner.

Cross-check: test each answer figure against these three forbidden pairs.

• Figure (1) shows F and B together, one of the forbidden pairs, so it cannot be formed.

• Figure (2) shows F, E, and D together, none of these three form a forbidden pair, so it is a valid cube.

• Figure (3) shows E and C together, one of the forbidden pairs, so it cannot be formed.

• Figure (4) shows A and D together, one of the forbidden pairs, so it cannot be formed.

Only the cube in figure (2) can be formed by folding sheet (X), so the answer is '2 only'.