Problems and Puzzles

Many people have long had a tendency to associate problems and puzzles with the 'Chinese' but nobody really knows why they have been given this East Asian origin. One suggestion is that perhaps the Europeans were inclined to ascribe puzzles the name of what was, to them, a puzzling civilization.

Diagram 13.Puzzle of the Rings.

The above picture describes the 'Puzzle of the Chinese Rings'. This problem was first found by Cardan but was later treated at length in mathematical terms by John Wallis in approximately 1685. Lastly, in the nineteenth century it was discussed using binary arithmetic notation by Gros.

This puzzle was commonly known in China, at the beginning of this century as 'Ring of Linked Rings' or in Chinese translation as Lien nuan chhuan

Another geometrical puzzle related to the Chinese in the rearrangement of a set of wooden pieces (a square, a rhombus and five triangles of different sizes). This puzzle is known as being one of the oldest amusements of the East. To the Chinese this puzzle is known as the 'Seven Subtle Shapes' or Chhi Chhiao. However, to the Europeans it was known as 'tangrams'. This puzzle is related to geometrical dissections, static games and also to the great wealth of geometrical forms employed by Chinese builders through the centuries in the lattice-work of windows.

Yet another puzzle, more related to the linked rings was the folding of paper (also known as che chih shu). This puzzle is also mentioned in the famous poem written by Tu Fu.

The last problem I wish to discuss is the most famous known as the problem of the 'hundred fouls', to solve it is necessary to use a determine analysis or the extracting of cube roots. The original problem form the fifth century read as follows: "a cock is worth 5 qian, a hen 3 qian and 3 chicks 1 qian; with 100 qian we buy 100 of them; how many cocks, hens and chicks are there?" (Grattan-Guinness, 1994, pg 96)

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