Tangram

The Tangram is a dissection puzzle consisting of seven flat geometric pieces, called "tans," that together form a square. The objective is to arrange all seven pieces — without overlapping — to form a specific silhouette shape. The pieces include two large right triangles, one medium right triangle, two small right triangles, one square, and one parallelogram. Hundreds of shapes can be formed, from animals and people to letters and abstract figures.

Rules

1. You are given a target silhouette (outline) to reproduce.
2. You must use all seven pieces — no more, no fewer.
3. Pieces must lie flat on the surface.
4. Pieces may not overlap.
5. Pieces may be rotated and flipped freely.
6. The completed arrangement must exactly fill the target silhouette.

The Seven Pieces

• 2 large right triangles (each is half the full square)
• 1 medium right triangle (one quarter of the full square)
• 2 small right triangles (each is one eighth of the full square)
• 1 square (one eighth of the full square)
• 1 parallelogram (one eighth of the full square) — the only piece that may need to be flipped

Strategies

• Start with the Big Pieces: The two large triangles take up the most area. Place them first to establish the broad outline of the shape.
• Identify Right Angles: Look for right-angle corners in the silhouette — these are often filled by triangle corners.
• Use the Parallelogram Last: The parallelogram is the trickiest piece because it is the only non-symmetric one (it can be flipped to its mirror image). Try other pieces first and use the parallelogram to fill what remains.
• Look for Familiar Sub-Shapes: Many silhouettes contain smaller squares, triangles, or rectangles that can be formed by known combinations of pieces.
• Count the Area: Each piece has a known fraction of the total area. If a region of the silhouette seems too large or too small for a piece, move on to a different placement.
• Edge Alignment: Pieces share a limited set of edge lengths. Matching edges of equal length often guides correct placement.

The Tangram is one of the oldest and most famous dissection puzzles in the world, originating in China during the late 18th century. Its Chinese name is "qi qiao ban" (七巧板), meaning "seven boards of skill" or "seven clever pieces."

The earliest known reference to the Tangram appears in a Chinese book from 1796 during the Qing Dynasty, though some historians believe the puzzle may be older. The puzzle became enormously popular in China and spread to Europe and America in the early 19th century. A major wave of "Tangram mania" swept through Europe around 1817, when trade ships brought the puzzle from Canton. Books of Tangram puzzles were published in multiple languages, and it became a fashionable parlor amusement among the upper classes. Napoleon Bonaparte is said to have been an avid Tangram player during his exile on St. Helena, though this claim is debated by historians.

The English name "Tangram" has uncertain origins. One theory attributes it to the obsolete English word "trangram" meaning a puzzle or trinket. Another suggests it derives from "Tang" (as in the Chinese dynasty) combined with the Greek suffix "-gram" (something written or drawn). Despite its ancient roots, the puzzle has never gone out of fashion.

In the 20th and 21st centuries, the Tangram has been widely adopted in education as a tool for teaching geometry, spatial reasoning, and problem-solving. Mathematician Fu Traing Wang and Chuan-Chih Hsiung proved in 1942 that there are only 13 convex shapes that can be formed with the seven Tangram pieces. The puzzle has inspired countless variations, digital apps, and competitions, and remains one of the most recognizable puzzles in the world.