Will This Net Make a Cube?

A flat shape can look perfectly tidy, yet fold into a jumble. The secret is not counting six squares. It is tracking where every face lands.

Start with one square as the base. Imagine its four edge-neighbours lifting through right angles, like walls around a room. Keep the base still. Follow each shared edge. A face may turn again through another hinge, but it cannot twist, stretch, or pass through a face already there. Now check the landing places. A finished cube needs one base, four different side faces, and one opposite face. If two squares try to cover the same side, the net fails. If a gap remains, it fails too. Be careful: squares far apart on the flat net are not automatically opposite. Folding changes their relationship. Judge them only after the hinges turn. You can rehearse each fold with your finger, ninety degrees at a time, while watching for an overlap.

Let's work through an example. You are shown two arrangements, A and B, each made from six equal unmarked squares. In both, four squares form a straight horizontal row. Which arrangement can fold into a cube? In A, one extra square sits above the second square in the row. The other sits below that same second square. Hold the second square as the base. Fold its left, right, upper, and lower neighbours upwards. They become four DIFFERENT walls. The fourth square in the row is hinged to the right wall. Fold it once more... it closes across the top, opposite the base. Every cube position is filled exactly once. A works. In B, both extra squares sit above the row: one above the second square, and one above the third. Fold the four-square strip around. Then lift both upper flaps. They aim for the SAME top position and overlap. So B cannot make a cube. The answer is A.

Remember: choose a base, turn each hinge through a right angle, and check every landing place. One face per position, with no gaps or overlaps - cube solved!