Puzzle Encyclopedia

A rigid-body disentanglement puzzle, typically made from iron or steel, in which a ring, loop, or other piece must be removed from a frame or second piece. The solution usually depends on finding the correct sequence of movements and orientations, taking advantage of gaps, curves, and openings that may not be obvious at first glance.

A disentanglement puzzle made from shaped or bent wire, usually involving two or more pieces that must be separated without bending or forcing them. Wire puzzles come in a wide variety of designs, from simple interlocking shapes to complicated arrangements requiring several carefully coordinated movements.

A sequential disentanglement puzzle in which a rigid loop or shuttle must be freed from a series of rings attached to a frame. The rings must be moved in a particular order, and some must be returned to their original positions before others can be released. The puzzle is closely related to binary arithmetic and Gray code. Under the standard convention of counting individual ring movements, the minimum number of moves for n rings is (2^(n+1) − 2)/3 when n is even, and (2^(n+1) − 1)/3 when n is odd.

A disentanglement puzzle involving a flexible loop, cord, or length of string that must be removed from or passed through another object. Solutions often depend on manipulating loops, passing folded sections of string through openings, or finding an unexpected way to move the string around an obstacle.

A puzzle consisting of a grid of numbered or pictured tiles with one empty space, in which tiles are moved by sliding them into the empty space. The goal is to reach a target arrangement. Exactly half of all starting configurations are solvable; the other half are in a separate parity class and cannot reach the goal state.

A puzzle consisting of a geometric solid divided into movable sections that rotate around one or more axes. The goal is to restore the puzzle to its intended solved arrangement after scrambling it. Twisty puzzles can be studied using group theory, and many are solved through sequences of moves known as algorithms.

A single-player puzzle played on a board with holes, in which a peg jumps over an adjacent peg into an empty hole, removing the peg it jumped over. The usual goal is to reduce the board to a single remaining peg. The standard English board has 33 holes, while the French or European board has 37. Mathematicians have studied the puzzle using methods that help determine which starting positions and finishing arrangements are possible.

A puzzle consisting of three pegs and a set of discs of different sizes. The goal is to move all discs from the first peg to the third, moving only one disc at a time and never placing a larger disc on a smaller one. The minimum number of moves for n discs is 2^n − 1. The puzzle was invented by Édouard Lucas in 1883.

An interlocking assembly puzzle commonly made from notched wooden sticks, often six, arranged to form a three-dimensional shape. The challenge may involve taking the puzzle apart, putting it back together, or both. Some burrs have a key piece that begins the disassembly, while others require several coordinated movements before a piece can be removed. Depending on the design, a burr may have one solution or several.

A mechanical puzzle made from pieces that fit together in a way that restricts their movement. Solving it may require finding a particular sequence of movements to separate or assemble the pieces. Burr puzzles are a well-known type of interlocking puzzle, but other designs use geometric solids, irregular shapes, or more elaborate mechanisms. Some interlocking puzzles are assigned a level based on the moves needed to release the first piece.

A puzzle in which a set of pieces must fit within a specified container, outline, or target shape without overlapping. Pieces may need to be rotated, rearranged, or placed in a particular order. Some packing puzzles have a unique solution, while others allow several different arrangements.

A puzzle in which a geometric shape is divided into pieces that can be rearranged to form another shape or a variety of target figures. The Tangram is one of the best-known examples. Another famous example is Henry Dudeney's haberdasher's puzzle, which demonstrates how an equilateral triangle can be dissected into four pieces that form a square.

AA puzzle consisting of pieces cut from a flat picture or design that must be assembled to recreate the complete image. Early examples included wooden dissected maps made by John Spilsbury in the 1760s. The name 'jigsaw puzzle' became associated with the pastime in the late nineteenth century, when mechanical saws were used to cut wooden puzzles. Today, most mass-produced jigsaws are die-cut from cardboard, although wooden puzzles remain popular.

A jigsaw piece cut into a recognizable shape — an animal, a letter, a tool — rather than the standard interlocking tab-and-blank form. Whimsy pieces are a feature of premium wooden jigsaw puzzles and are considered a mark of quality craftsmanship. They are typically hidden within the puzzle and discovered during assembly.

A jigsaw puzzle with an image or design printed on both sides of its pieces. The solver must determine which side of each piece belongs to the image being assembled, as well as where the piece fits. The two images may be related or entirely different, and similar colors or patterns on both sides can make the puzzle especially challenging.

A puzzle in which success depends partly or primarily on physical coordination and controlled movement. Common examples involve guiding balls or marbles into target positions by tilting, rotating, or carefully manipulating the puzzle. Some dexterity puzzles also require planning and experimentation to discover the best way to reach the goal.

A puzzle in which a path must be found through a network of passages from a start point to a goal. Physical maze puzzles require navigating a ball or token through a three-dimensional maze; paper mazes are solved by tracing. The tilting wooden labyrinth — a platform maze navigated by two knobs — is the canonical physical form.