10 November 2014
A popular Chinese game: the Qi Qiao Tu, or Tangram
Tangram is a simple yet very entertaining dissection puzzle game which involves 7 flat shapes and the player’s imagination. The aim of the game is to create figures of given silhouettes and its rules are simple: the player must use all seven pieces, without overlapping them, and every piece must touch at least one other. Tangram is still one of the most popular puzzle games in the world. It comes from China, where it is called 七巧图 (qi qiao tu) or 七巧板 (qi qiao ban), meaning "seven tablets of ability" and where it has a long tradition. The English has thought to have been derived from Tang, with reference to the Tang Dynasty, and the Greek suffix –gramma (graph). However, both the origin and the etymology of the English name remain uncertain.
Usually, the Chinese Tangram game books include, in two separate volumes, the silhouettes to be created and the solutions. In the picture below there is a pair of books published in China in 1815: the one on the top displays the silhouettes, the one below contains the corresponding solutions, which highlight the position of each of the seven pieces to produce the desired figure. Generally, the shapes are stylizations of common objects or animals.
Patterns from the 七巧图合璧 (Qi qiao tu he bi), Tangram puzzle book, China c. 1815 (British Library 15257.d.5) and below 七巧图解(Qi qiao tu jie), Tangram puzzle book solutions, China c. 1815 (British Library 15257.d.14)
The classic version of the Tangram comprises five triangles of different sizes, a square and a rhomboid which together form a square. Despite its simplicity (we can create a Tangram set to play with from a piece of paper, even though there are Tangram sets carved from precious jade or ivory), this game involves creativity and patience. Since its arrival in Europe it has been considered as an intellectual and challenging game both for children and adults. Much research has been conducted on the use of Tangram in the fields of mathematics, geometry, psychology and education.
The birth and development of Tangram and other visual games in China has been connected by some scholars to the 燕几圖 (Yan ji tu), commonly attributed to Huang Bo’en (1079 – 1118), which was transmitted during the Yuan and Ming dynasties in a collection called Xin shang Bian. The Yan ji tu is a monograph about the arrangements of tables for convivial gatherings. The text is very schematic and reduced to captions of a series of drawings showing seven geometrical table pieces in different arrangements.
Around the 1820s there was a craze for the Tangram in Europe, called at the time “Chinese enigma” or “Eastern Puzzle”. Its attraction lay in its exoticism and a fascination for everything coming from East Asia. The game was especially popular among the upper classes because, despite being a solitary game, it allowed players to compete with each other in solving the problems and could be used to entertain guests. Several manuals were published in England, France, Germany and Italy, with figures and solutions. The Eight Book of Tan by Sam Loyd, published in New York in 1903, made this traditional Chinese game popular in the Unites States and at the same time reinforced its popularity in Europe at the beginning of the 20th century.
Left: The Great Eastern Puzzle, London, 1817: English reproduction of the Chinese 七巧图合璧 Qi qiao tu he bi, with all the 316 original puzzles contained in the 1815 Chinese version. An English introduction was added (British Library 15257.d.13)
Right: First and second pages from the original Chinese version, 1815 (British Library 15257.d.5)
Another widespread guide, Le Véritable casse-tête, ou Énigmes chinoises, was published in Paris in 1820, and it testifies to the popularity of the game in France in that period. The fascination for Tangram included some famous personalities, among them, apparently, Napoleon and Edgar Allan Poe. Lewis Carroll, born Charles Lutwidge Dodgson, writer and mathematician, recreated the main characters of his novel Alice's Adventures in Wonderland using the seven pieces of Tangram.
Left: Introduction to the game and illustrations with figures from Le Véritable casse-tête, ou Énigmes chinoises, Paris, 1820 (British Library 1210.m.41)
Right, Tangram silhouettes from Lewis Carroll's Bedside Book - ‘Entertainments for the Wakeful Hours’, edited by Edgar Cuthwellis with illustrations by Lewis Carroll and Phuz (British Library X.529/34199)
Almost fifty years after the publication of the 七巧图合璧 (Qi qiao tu he bi) in 1815, Tong Xiegeng, a scholar from the city of Hangzhou, developed a new puzzle made of 15 pieces, six of which with curvilinear edges. This new version of the Tangram was called Yi zhi ban 益智板, or “Tablets for Enhancing Intelligence”. Tong Xiegeng published in 1862 a two volume book called Yi zhi tu 益智图, containing several puzzles to be solved with the fifteen pieces. These puzzles include scenes from classical Chinese poems or stories.
More recently Donald Verry took some beautiful pictures in the British Library building in St. Pancras and named two of them “Tangram”. Can you guess from which spot they were taken?
Bussotti, Michela, “Jeux de tables: le Yanji tu, livre sans texte d'«images en action»?”, in Bulletin de l'Ecole française d'Extrême-Orient, n. 89, 2002
Loyd, Sam, Sam Loyd's Book of Tangram Puzzles (The 8th Book of Tan Part I). Mineola, New York: Dover Publications, 1968
Read, Ronald C., Tangrams: 330 Puzzles, New York: Dover Publications, 1968
Slocum, Jerry, et al., The Tangram Book: The Story of the Chinese Puzzle with Over 2000 Puzzles to Solve. New York: Sterling Publishing Company, 2004
 See for example Fu, Traing Wang and Chuan-Chih, Hsiung, “A Theorem on the Tangram”, in The American Mathematical Monthly, Vol. 49, No. 9, 1942