The Tangram – Seven Boards of Cunning

The Tangram is a Chinese puzzle over a millennium old. It resembles the Western jigsaw puzzle, but differs from the same in always having seven pieces, which are fitted together in different ways to make an almost infinite number of different shapes. Each puzzle-game begins by posing or selecting a challenge–an outline or silhouette of a figure which is supposed to be the “solution” of the game. Make your solution by arranging the pieces of the tangram-set to attain a match with the given figure.

Several versions on its word etymology abound while its Chinese origin is almost uncontested. The most current version from Hanyu Pinyin (the romanization system for Chinese Mandarin developed by the People’s Republic of China) calls the tangram: qi quiao ban–and is translated to literally mean “seven boards of cunning.” Another version claims Tang is Cantonese for “Chinese” and Gram is for “something drawn”–therefore, “something Chinese drawn.”

To make a tangram, just get a square piece of material and cut it into five right-triangles (there will be three different sizes: with two for each of the smaller and bigger pieces), a square, and a rhomboid (also called a parallelogram). If you cannot make this out, just get yourself any illustrated English dictionary, and look up the word–tangram; most of the time, you will find an illustration with it. Alternatively, just browser-search the word on the Internet…

Aside from mandating that all seven pieces (called tans) are used to solve a puzzle, the rules of the game further require that none of the pieces overlap and that the tans are touching one another. Puzzles must comply with these tenets in order to be considered as official or “compliant” tangram puzzles.

Some of the puzzles currently offered include: geometric shapes, numerals and alphabetic characters; man-made objects such as houses, buildings, bridges; human figures in action, different animals in many poses, and others. An estimate is that there are 6.13 million possible “compliant” configurations–where “compliant” means that at least one edge and at least one vertex of any tan is matched to (or touching) an edge or the vertex (or tip) of another.

Convex shapes are tangram configurations where a line segment drawn between any two points on the shape always pass through the interior of the configuration. These are a few simple polygons, with no recesses on them; which have been proven to number only thirteen. This count includes just the following: one right-triangle, six quadrilaterals, two pentagons, and four hexagons.

Paradoxes are two similar shapes, with one being a derivative of the other; almost the same but distinctively different because the other has a part of it missing. The most common of this is the Dudeney paradox of two monks– where the other version has a foot missing.

Over all these years, the tangram has maintained its universal appeal as a worthy pastime and object of interest in art and design; while teaching geometric abstraction, proportion, and context.