Derived from the Greek word for '5', and "domino", a pentomino is a polyomino of order 5; that is, a polygon in the plane made of 5 equal-sized squares connected edge to edge. When rotations and reflections are not considered to be distinct shapes, there are 12 different free pentominoes. When reflections are considered distinct, there are 18 one-sided pentominoes. When rotations are also considered distinct, there are 63 fixed pentominoes.
The Rubik's Cube is a 3D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik to be sold by Pentangle Puzzles in the UK in 1978, and then by Ideal Toy Corp in 1980 via businessman Tibor Laczi and Seven Towns founder Tom Kremer. The cube was released internationally in 1980 and became one of the most recognized icons in popular culture. It won the 1980 German Game of the Year special award for Best Puzzle. As of January 2024, around 500 million cubes had been sold worldwide, making it the world's bestselling puzzle game and bestselling toy. The Rubik's Cube was inducted into the US National Toy Hall of Fame in 2014.
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 discover 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.
The Rubik's Revenge is a 4×4×4 version of the Rubik's Cube. It was released in 1981. Invented by Péter Sebestény, the cube was nearly called the Sebestény Cube until a somewhat last-minute decision changed the puzzle's name to attract fans of the original Rubik's Cube. Unlike the original puzzle, it has no fixed faces: the center faces are free to move to different positions.
The Pocket Cube is a 2×2×2 combination puzzle invented in 1970 by American puzzle designer Larry D. Nichols. The cube consists of 8 pieces, which are all corners.
The Professor's Cube is a 5×5×5 version of the original Rubik's Cube. It has qualities in common with both the 3×3×3 Rubik's Cube and the 4×4×4 Rubik's Revenge, and solution strategies for both can be applied.
The Pyraminx is a regular tetrahedron puzzle in the style of Rubik's Cube. It was made and patented by Uwe Mèffert after the original 3 layered Rubik's Cube by Ernő Rubik, and introduced by Tomy Toys of Japan in 1981.
The Square-1 is a variant of the Rubik's Cube. Its distinguishing feature among the numerous Rubik's Cube variants is that it can change shape as it is twisted, due to the way it is cut, thus adding an extra level of challenge and difficulty. The Super Square One and Square Two puzzles have also been introduced. The Super Square One has two additional layers that can be scrambled and solved independently of the rest of the puzzle, and the Square Two has extra cuts made to the top and bottom layer, making the edge and corner wedges the same size.
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.
The Pyramorphix, also called Pyramorphinx, is a tetrahedral puzzle similar to the Rubik's Cube. It has a total of 8 movable pieces to rearrange, compared to the 20 of the Rubik's Cube. Although it looks like a trivially simple version of the Pyraminx, it is an edge-turning puzzle with the mechanism identical to that of the Pocket Cube.
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. Generally, combination puzzles also include mathematically defined examples that have not been, or are impossible to, physically construct.
The Rubik's Cube is the original and best known of the three-dimensional sequential move puzzles. There have been many virtual implementations of this puzzle in software. It is a natural extension to create sequential move puzzles in more than three dimensions. Although no such puzzle could ever be physically constructed, the rules of how they operate are quite rigorously defined mathematically and are analogous to the rules found in three-dimensional geometry. Hence, they can be simulated by software. As with the mechanical sequential move puzzles, there are records for solvers, although not yet the same degree of competitive organisation.
The V-Cube 6 is a 6×6×6 version of the original Rubik's Cube. The first mass-produced 6×6×6 was invented by Panagiotis Verdes and is produced by the Greek company Verdes Innovations SA. Other such puzzles have since been introduced by a number of Chinese companies, most of which have mechanisms which improve on the original. Unlike the original puzzle, it has no fixed facets: the center facets are free to move to different positions.
The Impossiball is a rounded icosahedral puzzle similar to the Rubik's Cube. It has a total of 20 movable pieces to rearrange, which is the same as the Rubik's Cube, but all of the Impossiball's pieces are corners, like the Pocket Cube.
The V-Cube 7 is a combination puzzle in the form of a 7×7×7 cube. The first mass-produced 7×7×7 was invented by Panagiotis Verdes and is produced by the Greek company Verdes Innovations SA. Other such puzzles have since been introduced by a number of Chinese companies, some of which have mechanisms which improve on the original. Like the 5×5×5, the V-Cube 7 has both fixed and movable center facets.
The Void Cube is a 3-D mechanical puzzle similar to a Rubik's Cube, with the notable difference being that the center pieces are missing, which causes the puzzle to resemble a level 1 Menger sponge. The core used on the Rubik's Cube is also absent, creating holes straight through the cube on all three axes. Due to the restricted volume of the puzzle it employs an entirely different structural mechanism from a regular Rubik's Cube, though the possible moves are the same. The Void Cube was invented by Katsuhiko Okamoto. Gentosha Education, in Japan, holds the license to manufacture official Void Cubes. These official designs are also sold under the Rubik's brand, owned by Spin Master Ltd., and workalikes are available from a variety of manufacturers. Speed-solving the Void Cube is common in exhibition but is not an official World Cube Association competition event.
The Pyraminx Duo is a tetrahedral twisty puzzle in the style of the Rubik's Cube. It was suggested by Rob Stegmann, invented by Oskar van Deventer, and has now been mass-produced by Meffert's.
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 3×3×3 Rubik's Cube, which only has 6 different colours, the Nine-Colour Cube has 9 colours, with the individual pieces having one colour each.
The V-Cube 8 is an 8×8×8 version of the Rubik's Cube. Unlike the original puzzle, it has no fixed facets: the center facets are free to move to different positions. The design was covered by Panagiotis Verdes' patent from 2007 but Verdes Innovations SA did not produce it for sale until 2014. Other manufacturers released their own versions of the puzzle much earlier.
The Dino Cube is a cubic twisty puzzle in the style of the Rubik's Cube. It was invented in 1985 by Robert Webb, though it was not mass-produced until ten years later. It has a total of 12 external movable pieces to rearrange, compared to 20 movable pieces on the Rubik's Cube.
