Seven pieces, one square’s worth of space
A tangram set contains five triangles, one square, and one parallelogram. Together, the pieces can be fitted back into a square, but the puzzle becomes more interesting when they are rearranged to make a new outline: a person, animal, or object, for example. In a traditional silhouette puzzle, all seven pieces must be used, with none overlapping or left out.
The pieces are often called tans. Their straight edges meet at angles that make the set unusually versatile: triangles can join into larger triangles, while the square and parallelogram can fill gaps between them. Every design must use exactly the same total area, so the challenge is not to find extra space but to distribute the pieces in a shape that still reads clearly from its outline.
The hidden constraint in a silhouette
A tangram picture usually gives no internal lines to show where one piece ends and another begins. Solvers have to infer those boundaries from the outer contour, then test how the pieces might fit inside it. A shape that looks obvious at first can require a surprising rearrangement—especially because the parallelogram may need to be turned over to face the opposite way.
That constraint explains the puzzle’s lasting appeal. The same small inventory can suggest many different images, but each image has to obey the same geometry. The broken-square story is memorable partly because it captures that transformation: a whole becomes pieces, and the pieces become a new whole.
