The story in three lines. Lan and Inkling fold Kami into a cup and step into a college room at Princeton in 1939, where Rosa has three pictures for her brother's birthday and a card with only two sides. Lan folds a strip of ten triangles on every line and gets a stiff stick, until Mark reads the drawing: fold after the third triangle, after the sixth, and tuck the last one behind. The strip becomes a hexagon that keeps a third face hidden inside.

One question to ask. "Why did the last triangle have to go behind?" The answer the story wants: it has to lie flat against the first triangle so it can be glued; folded to the front, it sits on top of the wrong triangle.

One thing to do at the table. Fold one with the steps on our flexagon page. Colour each face a different colour before you flex: front, back, then the face that appears. Count the triangles on one face, then count all the sides of the nine triangles. Ask how eighteen sides can make only three faces.

The grown-up layer. Arthur Stone, a student from England, found the flexagon in 1939 by folding the strips he trimmed off American notebook paper to fit his English binder. With Bryant Tuckerman, Richard Feynman and John Tukey he formed the Princeton Flexagon Committee, and Tuckerman drew the first map of how the faces connect. Martin Gardner's 1956 article about them began his famous column of mathematical games.

Let your child tell the story back in their own words first.