Rules

1. Use all seven pieces; no more, no fewer.
2. Pieces must not overlap (edge or corner contact is allowed).
3. Pieces must connect (vertex, edge, or mixed contact).
4. Play in a single plane.
5. The outer silhouette must match the target; total area equals the original square.

Allowed moves

How to play

1. Take out all seven pieces.
2. Read the target: full diagram (guided) or outline silhouette only.
3. Move pieces into the target area; rotate as needed; flip only if the puzzle allows.
4. Fit pieces with no overlap until the silhouette is filled.
5. Confirm all seven pieces are used and the outline matches — done.

Pieces

Together the seven pieces form the original square.

Play modes

You can also play Tangram online.

(1) Song banquet tables (yanji)

Chinese histories often open with the Song-dynasty Yanjitu (“Banquet Table Diagrams”): a set of rectangular low tables in a few fixed lengths that hosts rearranged to seat different numbers of guests—first six tables, later seven under the name “Seven Stars.” Tradition credits Huang Bosi (1079–1118); bibliographic notes question the preface dating and signature style, and some catalogue discussions allow a later attribution. Yanji is furniture-scale recreational arrangement—the idea that fixed parts can form many flat plans—and a common precursor narrative for Tangram. It is not evidence that the modern seven-piece wooden set already existed in the Song.

(2) Ming butterfly-wing tables (dieji)

In the Ming, dieji / “butterfly-wing” tables kept the rearrangeable-furniture idea but switched to right triangles, trapezoids, and similar angled pieces—about thirteen boards in many accounts—said to join like butterfly wings and, when taken apart, to yield a hundred-plus figures. Yan Cheng (嚴澄／嚴瀓) and Ge Shan’s Dieji pu (c. 1617) are the usual citations. The Qing miscellany Lenglu zashi by Lu Yitian sketches the line of descent as yanji → dieji → “of late there is also the qiqiao diagram… seven pieces, with variations numbering more than a thousand.” Butterfly tables supply the near-source narrative for a silhouette-dissection pastime.

(3) Qing standardization and Qiqiao tu hebi (1813)

Once the seven small wooden pieces settled into the familiar inventory—five isosceles right triangles (two large, one medium, two small), one square, and one parallelogram—the puzzle we call Tangram was in place. The secure documentary anchor is the Jiaqing 18 (1813) album Qiqiao tu hebi (“Complete Tangram Diagrams”); prefaces and colophons often carry pen names such as Sang Xia Ke (“Guest under the Mulberry”) and Bi Wu Jushi (“Scholar of the Green Parasol”). Later Qing collections include Yangxin tang qiqiao tu and Wen Shaotang qiqiao xu tu. The Palace Museum holds a wooden Qiqiao tu set whose label notes the yanji / dieji lineage. An ivory export set reportedly inscribed for Francis Waln in Canton, April 1802, shows that trade pieces were already circulating around the time of the early albums.

(4) Western craze (c. 1817–1820)

Through Canton and other ports, sets and picture books reached Europe and North America. In roughly 1817–1820, tangram albums appeared in rapid succession in England, France, the German states, Italy, the Low Countries, Scandinavia, and the United States—the first international puzzle craze of its kind. Western writers often filed Tangram with other “Chinese puzzles” such as the nine linked rings. Anecdotes that Napoleon passed exile hours on St Helena with a Tangram set circulate widely; puzzle historians treat them as unverified colour, not hard fact. The English word tangram is attested by the mid-nineteenth century (Thomas Hill’s 1848 geometry pamphlet is a frequently cited early use).

(5) Sam Loyd’s invented antiquity

English-language popular history was long coloured by Sam Loyd’s The Eighth Book of Tan (1903; often dated 1908 in secondary lists): a lavish pattern book wrapped in a spoof “Book of Tan” mythology that pushed the invention back four thousand years to a god named Tan. By about 1910, Oxford English Dictionary editor Sir James Murray and Chinese scholars consulting for Henry Dudeney had shown that “Tan,” the god, and the Book of Tan were unknown to Chinese literature or tradition. The figures remain useful; the origin tale does not.

(6) Japan’s Sei Shōnagon chie-no-ita (1742)

Japan’s Sei Shōnagon’s ingenuity pieces (preface 1742) is also a seven-piece square dissection for silhouette play, but the cut differs from the Chinese standard set and includes hollow-outline challenges. Because that date precedes the surviving Chinese 1813 album, invention-priority debates appear in comparative writing. This encyclopedia presents both lines side by side and does not decree a single inventor. (Qing Tong Yegeng’s fifteen-piece Yizhi tu is a different toy; the shared Chinese label “wisdom diagram” should not be conflated with the seven-piece Tangram.)

Yanji / dieji / Tangram at a glance

Sources

1. ChinesePuzzles.org, Tangram Puzzle
2. Tian, Art and Mathematics of Tangrams, Bridges 2012
3. Walravens, Early History of the Tangram in Germany, CFF 72
4. Palace Museum, notes on Qiqiao tu / Yizhi tu
5. chinaknowledge.de, Yanjitu
6. English Wikipedia, Tangram
7. The Conversation, history and mystery of Tangram (2022)
8. Sam Loyd, The 8th Book of Tan (Dover reprint on Internet Archive)
9. Lu Yitian, Lenglu zashi (yanji → dieji → qiqiao)
10. Wang & Hsiung, A Theorem on the Tangram, American Mathematical Monthly 1942