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Disentanglement puzzles (also called entanglement puzzles, tanglement puzzles, tavern puzzles or topological puzzles) [1] are a type or group of mechanical puzzle that involves disentangling one piece or set of pieces from another piece or set of pieces. Several subtypes are included under this category, the names of which are sometimes used synonymously for the group: wire puzzles; nail puzzles; ring-and-string puzzles; et al. [2] [3] Although the initial object is disentanglement, the reverse problem of reassembling the puzzle can be as hard as—or even harder than—disentanglement. There are several different kinds of disentanglement puzzles, though a single puzzle may incorporate several of these features. [4]
Wire-and-string puzzles usually consist of:
One can distinguish three subgroups of wire-and-string puzzles:
One particularly difficult puzzle was designed by R. Boomhower in 1966 and has been modified into different designs (but topologically similar). Different versions include a paddle-shaped design, a vertical beam on a wood support, and two vertical beams on a wood support. Variations also have the string passing through the slot once or two times. Names have included the Boomhower puzzle, T-Bar puzzle, Wit's End puzzle, and the Mini Rope Bridge puzzle. Some sources identify a topologically-equivalent puzzle called the Mystery Key issued by the Peter Pan company in the 1950s. [5] [6] [7] [8] [9]
Wire puzzles, or nail puzzles consist of two or more entangled pieces of more or less stiff wire, metal rods, or bent nails. The pieces may or may not be closed loops. The closed pieces might be simple rings or have more complex shapes. Normally the puzzle must be solved by disentangling the two pieces without bending or cutting the wires. [10]
Early wire puzzles were made from bent carpenter's nails, horseshoes, or similar material. [11]
A plate-and-ring puzzle usually consists of three pieces:
The plate as well as the ring are usually made from metal. The ring has to be disentangled from the plate. [12]
Some puzzles have been created which may appear deceptively simple, but are actually impossible to solve. One such puzzle is the "Notorious Figure Eight Puzzle" (also called the "Figure Eight Puzzle, or "Possibly Impossible"). It is sometimes sold with instructions giving hints as to its level of difficulty, and a "solution" is provided but is vague and impossible to follow, but the puzzle is actually impossible to solve. [13] [14]
Most puzzle solvers try to solve such puzzles by mechanical manipulation, but some branches of mathematics can be used to create a model of disentanglement puzzles. Applying a configuration space with a topological framework is an analytical method to gain insight into the properties and solution of some disentanglement puzzles. However, some mathematicians have stated that capturing the important aspects of many such puzzles can often be difficult, and there is no universal algorithm that will provide the solution generally to such puzzles. [1]
In mathematics, topology is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.
A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge. In a puzzle, the solver is expected to put pieces together in a logical way, in order to arrive at the correct or fun solution of the puzzle. There are different genres of puzzles, such as crossword puzzles, word-search puzzles, number puzzles, relational puzzles, and logic puzzles. The academic study of puzzles is called enigmatology.
A mechanical puzzle is a puzzle presented as a set of mechanically interlinked pieces in which the solution is to manipulate the whole object or parts of it. While puzzles of this type have been in use by humanity as early as the 3rd century BC, one of the most well-known mechanical puzzles of modern day is the Rubik's Cube, invented by the Hungarian architect Ernő Rubik in 1974. The puzzles are typically designed for a single player, where the goal is for the player to see through the principle of the object, rather than accidentally coming up with the right solution through trial and error. With this in mind, they are often used as an intelligence test or in problem solving training.
A burr puzzle is an interlocking puzzle consisting of notched sticks, combined to make one three-dimensional, usually symmetrical unit. These puzzles are traditionally made of wood, but versions made of plastic or metal can also be found. Quality burr puzzles are usually precision-made for easy sliding and accurate fitting of the pieces. In recent years the definition of "burr" is expanding, as puzzle designers use this name for puzzles not necessarily of stick-based pieces.
A shackle, also known as a gyve, is a U-shaped piece of metal secured with a clevis pin or bolt across the opening, or a hinged metal loop secured with a quick-release locking pin mechanism. The term also applies to handcuffs and other similarly conceived restraint devices that function in a similar manner. Shackles are the primary connecting link in all manner of rigging systems, from boats and ships to industrial crane rigging, as they allow different rigging subsets to be connected or disconnected quickly. A shackle is also the similarly shaped piece of metal used with a locking mechanism in padlocks. A carabiner is a type of shackle used in mountaineering.
Topological defects or solitons are irregularities or disruptions that occur within continuous fields or ordered states of matter. These defects, which can take various forms such as points, lines, or surfaces, are characterized by their stability and the fact that they cannot be 'smoothed out' or removed through continuous transformations of the field or material. They play a significant role in various areas of physics, including condensed matter physics, cosmology, and quantum field theory, and can have profound effects on the properties and behavior of the systems in which they occur.
The 15 Puzzle is a sliding puzzle which has 15 square tiles numbered 1 to 15 in a frame that is 4 tile positions high and 4 positions wide, with one unoccupied position. Tiles in the same row or column of the open position can be moved by sliding them horizontally or vertically, respectively. The goal of the puzzle is to place the tiles in numerical order.
The Megaminx or Mégaminx is a dodecahedron-shaped puzzle similar to the Rubik's Cube. It has a total of 50 movable pieces to rearrange, compared to the 20 movable pieces of the Rubik's Cube.
A sliding puzzle, sliding block puzzle, or sliding tile puzzle is a combination puzzle that challenges a player to slide pieces along certain routes to establish a certain end-configuration. The pieces to be moved may consist of simple shapes, or they may be imprinted with colours, patterns, sections of a larger picture, numbers, or letters.
Baguenaudier, also known as the Chinese rings, Cardan's suspension, Cardano's rings, Devil's needle or five pillars puzzle, is a disentanglement puzzle 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.
Slitherlink is a logic puzzle developed by publisher Nikoli.
The T puzzle is a tiling puzzle consisting of four polygonal shapes which can be put together to form a capital T. The four pieces are usually one isosceles right triangle, two right trapezoids and an irregular shaped pentagon.
An eye bolt is a bolt with a loop at one end. They are used to firmly attach a securing eye to a structure, so that ropes or cables may then be tied to it.
A combination puzzle, also known as a sequential move puzzle, is a puzzle which consists of a set of pieces which can be manipulated into different combinations by a group of operations. Many such puzzles are mechanical puzzles of polyhedral shape, consisting of multiple layers of pieces along each axis which can rotate independently of each other. Collectively known as twisty puzzles, the archetype of this kind of puzzle is the Rubik's Cube. Each rotating side is usually marked with different colours, intended to be scrambled, then 'solved' by a sequence of moves that sort the facets by colour. As a generalisation, combination puzzles also include mathematically defined examples that have not been, or are impossible to, physically construct.
String is a long flexible structure made from fibers twisted together into a single strand, or from multiple such strands which are in turn twisted together. String is used to tie, bind, or hang other objects. It is also used as a material to make things, such as textiles, and in arts and crafts. String is a simple tool, and its use by humans is known to have been developed tens of thousands of years ago. In Mesoamerica, for example, string was invented some 20,000 to 30,000 years ago, and was made by twisting plant fibers together. String may also be a component in other tools, and in devices as diverse as weapons, musical instruments, and toys.
The Challenge: Invasion of the Champions is the 29th season of the MTV reality game show, The Challenge. The new individual format was filmed in Krabi, Thailand during October and November 2016, and features alumni from The Real World, Road Rules, The Challenge, and Are You the One? competing.
The Nine-Colour Cube is a cubic twisty puzzle. It was invented in 2005 by Milan Vodicka and mass-produced by Meffert's seven years later. Mechanically, the puzzle is identical to the Rubik's Cube; however, unlike the Rubik's Cube, which only has 6 different colours, the Nine-Colour Cube has 9 colours, with the individual pieces having one colour each.