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Conway Puzzle
Conway's puzzle, or blocks-in-a-box, is a packing problem using rectangular blocks, named after its inventor, mathematician John Conway. It calls for packing thirteen 1 × 2 × 4 blocks, one 2 × 2 × 2 block, one 1 × 2 × 2 block, and three 1 × 1 × 3 blocks into a 5 × 5 × 5 box. Solution The solution of the Conway puzzle is straightforward once one realizes, based on parity considerations, that the three 1 × 1 × 3 blocks need to be placed so that precisely one of them appears in each 5 × 5 × 1 slice of the cube.Elwyn R. Berlekamp, John H. Conway and Richard K. Guy: winning ways for your mathematical plays, 2nd ed, vol. 4, 2004. This is analogous to similar insight that facilitates the solution of the simpler Slothouber–Graatsma puzzle. See also * Soma cube The Soma cube is a solid dissection puzzle invented by Danish polymath Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg. Seven pieces made out of unit cubes must be as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conway Puzzle Pieces
Conway may refer to: Places United States * Conway, Arkansas * Conway County, Arkansas * Lake Conway, Arkansas * Conway, Florida * Conway, Iowa * Conway, Kansas * Conway, Louisiana * Conway, Massachusetts * Conway, Michigan * Conway Township, Michigan * Conway, Missouri * Conway, New Hampshire, a New England town ** Conway (CDP), New Hampshire, village in the town * Conway, North Dakota * Conway, North Carolina * Conway, Pennsylvania * Conway, South Carolina * Conway River (Virginia) * Conway, Washington Elsewhere * Conway, Queensland, a locality in the Whitsunday Region, Queensland, Australia * Conway River (New Zealand) * Conway, Wales, now spelt Conwy, a town with a castle in North Wales * River Conway, Wales, similarly respelt River Conwy Ships * HMS ''Conway'' (school ship) * HMS ''Conway'' (1832), a 26-gun sixth rate launched in 1832 * USS ''Conway'' (DD-70) or USS ''Craven'' (DD-70), a Caldwell class destroyer launched in 1918 * USS ''Conway'' (DD-50 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Packing Problem
Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to either pack a single container as densely as possible or pack all objects using as few containers as possible. Many of these problems can be related to real-life packaging, storage and transportation issues. Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap. In a bin packing problem, you are given: * A ''container'', usually a two- or three-dimensional convex region, possibly of infinite size. Multiple containers may be given depending on the problem. * A set of ''objects'', some or all of which must be packed into one or more containers. The set may contain different objects with their sizes specified, or a single object of a fixed dimension that can be used repeatedly. Usually the packi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Horton Conway
John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches of recreational mathematics, most notably the invention of the cellular automaton called the Game of Life. Born and raised in Liverpool, Conway spent the first half of his career at the University of Cambridge before moving to the United States, where he held the John von Neumann Professorship at Princeton University for the rest of his career. On 11 April 2020, at age 82, he died of complications from COVID-19. Early life and education Conway was born on 26 December 1937 in Liverpool, the son of Cyril Horton Conway and Agnes Boyce. He became interested in mathematics at a very early age. By the time he was 11, his ambition was to become a mathematician. After leaving sixth form, he studied mathematics at Gonville and Caius College, Camb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conway Puzzle Hint
Conway may refer to: Places United States * Conway, Arkansas * Conway County, Arkansas * Lake Conway, Arkansas * Conway, Florida * Conway, Iowa * Conway, Kansas * Conway, Louisiana * Conway, Massachusetts * Conway, Michigan * Conway Township, Michigan * Conway, Missouri * Conway, New Hampshire, a New England town ** Conway (CDP), New Hampshire, village in the town * Conway, North Dakota * Conway, North Carolina * Conway, Pennsylvania * Conway, South Carolina * Conway River (Virginia) * Conway, Washington Elsewhere * Conway, Queensland, a locality in the Whitsunday Region, Queensland, Australia * Conway River (New Zealand) * Conway, Wales, now spelt Conwy, a town with a castle in North Wales * River Conway, Wales, similarly respelt River Conwy Ships * HMS ''Conway'' (school ship) * HMS ''Conway'' (1832), a 26-gun sixth rate launched in 1832 * USS ''Conway'' (DD-70) or USS ''Craven'' (DD-70), a Caldwell class destroyer launched in 1918 * USS ''Conway'' (DD-50 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parity (mathematics)
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not.. For example, −4, 0, 82 are even because \begin -2 \cdot 2 &= -4 \\ 0 \cdot 2 &= 0 \\ 41 \cdot 2 &= 82 \end By contrast, −3, 5, 7, 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201. See the section "Higher mathematics" below for some extensions of the notion of parity to a larger class of "numbers" or in other more general settings. Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slothouber–Graatsma Puzzle
The Slothouber–Graatsma puzzle is a packing problem that calls for packing six 1 × 2 × 2 blocks and three 1 × 1 × 1 blocks into a 3 × 3 × 3 box. The solution to this puzzle is unique ( up to mirror reflections and rotations). It was named after its inventors Jan Slothouber and William Graatsma. The puzzle is essentially the same if the three 1 × 1 × 1 blocks are left out, so that the task is to pack six 1 × 2 × 2 blocks into a cubic box with volume 27. Solution The solution of the Slothouber–Graatsma puzzle is straightforward when one realizes that the three 1 × 1 × 1 blocks (or the three holes) need to be placed along a body diagonal of the box, as each of the 3 x 3 layers in the various directions needs to contain such a unit block. This follows from parity considerations, because the larger blocks can only fill an even number of the 9 cells in each 3 x 3 layer.Elwyn R. Berlekamp, John H. Conway and Richard K. Guy: Winning ways for your mathematical plays, 2nd ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conway Puzzle Solution
Conway may refer to: Places United States * Conway, Arkansas * Conway County, Arkansas * Lake Conway, Arkansas * Conway, Florida * Conway, Iowa * Conway, Kansas * Conway, Louisiana * Conway, Massachusetts * Conway, Michigan * Conway Township, Michigan * Conway, Missouri * Conway, New Hampshire, a New England town ** Conway (CDP), New Hampshire, village in the town * Conway, North Dakota * Conway, North Carolina * Conway, Pennsylvania * Conway, South Carolina * Conway River (Virginia) * Conway, Washington Elsewhere * Conway, Queensland, a locality in the Whitsunday Region, Queensland, Australia * Conway River (New Zealand) * Conway, Wales, now spelt Conwy, a town with a castle in North Wales * River Conway, Wales, similarly respelt River Conwy Ships * HMS ''Conway'' (school ship) * HMS ''Conway'' (1832), a 26-gun sixth rate launched in 1832 * USS ''Conway'' (DD-70) or USS ''Craven'' (DD-70), a Caldwell class destroyer launched in 1918 * USS ''Conway'' (DD-50 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soma Cube
The Soma cube is a solid dissection puzzle invented by Danish polymath Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg. Seven pieces made out of unit cubes must be assembled into a 3×3×3 cube. The pieces can also be used to make a variety of other 3D shapes. The pieces of the Soma cube consist of all possible combinations of three or four unit cubes, joined at their faces, such that at least one inside corner is formed. There is one combination of three cubes that satisfies this condition, and six combinations of four cubes that satisfy this condition, of which two are mirror images of each other (see Chirality). Thus, 3 + (6 × 4) is 27, which is exactly the number of cells in a 3×3×3 cube. The Soma cube was popularized by Martin Gardner in the September 1958 Mathematical Games column in ''Scientific American.'' The book '' Winning Ways for your Mathematical Plays'' also contains a detailed analysis of the Soma cube problem. Ther ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Packing Problems
Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to either pack a single container as densely as possible or pack all objects using as few containers as possible. Many of these problems can be related to real-life packaging, storage and transportation issues. Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap. In a bin packing problem, you are given: * A ''container'', usually a two- or three-dimensional convex region, possibly of infinite size. Multiple containers may be given depending on the problem. * A set of ''objects'', some or all of which must be packed into one or more containers. The set may contain different objects with their sizes specified, or a single object of a fixed dimension that can be used repeatedly. Usually the packing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recreational Mathematics
Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited to being an endeavor for amateurs, many topics in this field require no knowledge of advanced mathematics. Recreational mathematics involves mathematical puzzles and games, often appealing to children and untrained adults, inspiring their further study of the subject. The Mathematical Association of America (MAA) includes recreational mathematics as one of its seventeen Special Interest Groups, commenting: Mathematical competitions (such as those sponsored by mathematical associations) are also categorized under recreational mathematics. Topics Some of the more well-known topics in recreational mathematics are Rubik's Cubes, magic squares, fractals, logic puzzles and mathematical chess problems, but this area of mathematics incl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tiling Puzzles
{{disambiguation, surname ...
Tiling may refer to: *The physical act of laying tiles *Tessellations Computing *The compiler optimization of loop tiling *Tiled rendering, the process of subdividing an image by regular grid *Tiling window manager People *Heinrich Sylvester Theodor Tiling (1818–1871), physician and botanist *Reinhold Tiling (1893–1933), German rocket pioneer Other uses *Neuronal tiling *Tile drainage, an agriculture practice that removes excess water from soil *Tiling (crater), a small, undistinguished crater on the far side of the Moon See also *Brickwork *Packing (other) *Tiling puzzle Tiling puzzles are puzzles involving two-dimensional packing problems in which a number of flat shapes have to be assembled into a larger given shape without overlaps (and often without gaps). Some tiling puzzles ask you to dissect a given ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanical Puzzle Cubes
Mechanical may refer to: Machine * Machine (mechanical), a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement * Mechanical calculator, a device used to perform the basic operations of arithmetic * Mechanical energy, the sum of potential energy and kinetic energy * Mechanical system, a system that manages the power of forces and movements to accomplish a task * Mechanism (engineering), a portion of a mechanical device Other * Mechanical (character), one of several characters in Shakespeare's ''A Midsummer Night's Dream'' * A kind of typeface in the VOX-ATypI classification See also * Machine, especially in opposition to an electronic item * ''Mechanical Animals'', the third full-length studio release by Marilyn Manson * Manufactured or artificial, especially in opposition to a biological or natural component * Automation, using machine decisions and processing instead of human * Mechanization, using machine labor in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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