Baguenaudier (; French for "time-waster"), also known as the Chinese rings, Cardan's suspension, Cardano's rings, Devil's needle or five pillars puzzle, is a

disentanglement puzzle Disentanglement puzzles (also called entanglement puzzles, tanglement puzzles, tavern puzzles or topological puzzles) are a type or group of mechanical puzzle that involves disentangling one piece or set of pieces from another piece or set of piec ...

featuring a loop which must be disentangled from a sequence of rings on interlinked pillars. The loop can be either string or a rigid structure. It is thought to have been

invent An invention is a unique or novel device, method, composition, idea or process. An invention may be an improvement upon a machine, product, or process for increasing efficiency or lowering cost. It may also be an entirely new concept. If an ...

ed originally in China. The origins are obscure. The American ethnographer

Stewart Culin Stewart Culin (July 13, 1858 – April 8, 1929) was an American ethnographer and author interested in games, art and dress. Culin played a major role in the development of ethnography, first concentrating his efforts on studying the Asian-Amer ...

related a tradition attributing the puzzle's invention to the 2nd/3rd century Chinese general

Zhuge Liang Zhuge Liang ( zh, t=諸葛亮 / 诸葛亮) (181 – September 234), courtesy name Kongming, was a Chinese statesman and military strategist. He was chancellor and later regent of the state of Shu Han during the Three Kingdoms period. He is ...

. It was used by French peasants as a locking mechanism. Variations of this include the ''Devil's staircase'', ''Devil's Halo'' and the ''impossible staircase''. Another similar puzzle is the ''Giant's causeway'' which uses a separate pillar with an embedded ring.

Mathematical solution

The 19th-century French mathematician

Édouard Lucas __NOTOC__ François Édouard Anatole Lucas (; 4 April 1842 – 3 October 1891) was a French mathematician. Lucas is known for his study of the Fibonacci sequence. The related Lucas sequences and Lucas numbers are named after him. Biography Lucas ...

, the inventor of the

Tower of Hanoi The Tower of Hanoi (also called The problem of Benares Temple or Tower of Brahma or Lucas' Tower and sometimes pluralized as Towers, or simply pyramid puzzle) is a mathematical game or puzzle consisting of three rods and a number of disks of v ...

puzzle, was known to have come up with an elegant solution which used

binary Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that ta ...

and

Gray codes The reflected binary code (RBC), also known as reflected binary (RB) or Gray code after Frank Gray, is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit). For example, the representat ...

, in the same way that his puzzle can be solved. The minimum number of moves to solve an ''n''-ringed problem has been found to be :

a(n) = \begin
  \dfrac & \textn\text \\
  \dfrac & \textn\text
\end

For other formulae, see .

References

{{reflist Chinese ancient games Chinese inventions Educational toys Mechanical puzzles

Mathematical solution

See also

References