Henry Ernest Dudeney/Modern Puzzles/146 - The Cardboard Box

Modern Puzzles by Henry Ernest Dudeney: $146$

The Cardboard Box

If I have a closed cubical cardboard box, by running the penknife along seven of the twelve edges (it must always be seven)

I can lay it out in one flat piece in various shapes.

Thus, in the diagram, if I pass the knife along the darkened edges and down the invisible edge indicated by the dotted line, I get the shape $A$.

Another way of cutting produces $B$ or $C$.

It will be seen that $D$ is simply $C$ turned over, so we will not call that a different shape.

Now, how many shapes can be produced?

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Geometrical Problems: Various Geometrical Puzzles: $146$. -- The Cardboard Box
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Geometrical Problems: Solid Geometry Puzzles: $316$. The Cardboard Box