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Eight queens puzzle

Index Eight queens puzzle

The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other. [1]

59 relations: Algorithm, Algorithms + Data Structures = Programs, Association for the Advancement of Artificial Intelligence, Backtracking, Bishop (chess), Bitwise operation, Brute-force search, Carl Friedrich Gauss, Chess, Chess composer, Chessboard, Clay Mathematics Institute, Combination, Constraint programming, Depth-first search, Determinant, Edsger W. Dijkstra, Exact cover, Factorial, Fairy chess piece, Genetic algorithm, George Pólya, Greedy algorithm, Heuristic, James Whitbread Lee Glaisher, Journal of Artificial Intelligence Research, King (chess), Knight (chess), Latin square, Logic programming, Magic square, Martin Richards (computer scientist), Mathematical game, Mathematical induction, Mathematical puzzle, Mathematician, Max Bezzel, Millennium Prize Problems, Min-conflicts algorithm, Niklaus Wirth, No-three-in-line problem, NP-completeness, Ole-Johan Dahl, Partial permutation, Pascal (programming language), Permutation, Permutation matrix, Queen (chess), Recursion, Rook (chess), ..., Rook polynomial, Search tree, Sharp-P-complete, Structured programming, Sudoku, Symmetry, Tony Hoare, Torus, W. W. Rouse Ball. Expand index (9 more) »

Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

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Algorithms + Data Structures = Programs

Algorithms + Data Structures.

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Association for the Advancement of Artificial Intelligence

The Association for the Advancement of Artificial Intelligence (AAAI) is an international, nonprofit, scientific society devoted to promote research in, and responsible use of, artificial intelligence.

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Backtracking

Backtracking is a general algorithm for finding all (or some) solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons a candidate ("backtracks") as soon as it determines that the candidate cannot possibly be completed to a valid solution.

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Bishop (chess)

A bishop (♗,♝) is a piece in the board game of chess.

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Bitwise operation

In digital computer programming, a bitwise operation operates on one or more bit patterns or binary numerals at the level of their individual bits.

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Brute-force search

In computer science, brute-force search or exhaustive search, also known as generate and test, is a very general problem-solving technique that consists of systematically enumerating all possible candidates for the solution and checking whether each candidate satisfies the problem's statement.

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Carl Friedrich Gauss

Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.

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Chess

Chess is a two-player strategy board game played on a chessboard, a checkered gameboard with 64 squares arranged in an 8×8 grid.

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Chess composer

A chess composer is a person who creates endgame studies or chess problems.

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Chessboard

A chessboard is the type of checkerboard used in the board game chess, consisting of 64 squares (eight rows and eight columns).

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Clay Mathematics Institute

The Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Peterborough, New Hampshire, United States.

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Combination

In mathematics, a combination is a selection of items from a collection, such that (unlike permutations) the order of selection does not matter.

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Constraint programming

In computer science, constraint programming is a programming paradigm wherein relations between variables are stated in the form of constraints.

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Depth-first search

Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures.

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Determinant

In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.

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Edsger W. Dijkstra

Edsger Wybe Dijkstra (11 May 1930 – 6 August 2002) was a Dutch systems scientist, programmer, software engineer, science essayist, and early pioneer in computing science.

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Exact cover

In mathematics, given a collection \mathcal of subsets of a set X, an exact cover is a subcollection \mathcal^* of \mathcal such that each element in X is contained in exactly one subset in \mathcal^*.

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Factorial

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.

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Fairy chess piece

A fairy chess piece, variant chess piece, unorthodox chess piece, or heterodox chess piece is a chess piece not used in conventional chess but incorporated into certain chess variants and some chess problems.

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Genetic algorithm

In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA).

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George Pólya

George Pólya (Pólya György; December 13, 1887 – September 7, 1985) was a Hungarian mathematician.

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Greedy algorithm

A greedy algorithm is an algorithmic paradigm that follows the problem solving heuristic of making the locally optimal choice at each stage with the intent of finding a global optimum.

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Heuristic

A heuristic technique (εὑρίσκω, "find" or "discover"), often called simply a heuristic, is any approach to problem solving, learning, or discovery that employs a practical method, not guaranteed to be optimal, perfect, logical, or rational, but instead sufficient for reaching an immediate goal.

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James Whitbread Lee Glaisher

James Whitbread Lee Glaisher FRS FRSE FRAS (5 November 1848, Lewisham – 7 December 1928, Cambridge), son of James Glaisher the meteorologist and Cecilia Glaisher the photographer, was a prolific English mathematician and astronomer.

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Journal of Artificial Intelligence Research

The Journal of Artificial Intelligence Research is an open access peer-reviewed scientific journal covering research in all areas of artificial intelligence.

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King (chess)

In chess, the king (♔,♚) is the most important piece.

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Knight (chess)

The knight (♘ ♞) is a piece in the game of chess, representing a knight (armored cavalry).

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Latin square

In combinatorics and in experimental design, a Latin square is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column.

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Logic programming

Logic programming is a type of programming paradigm which is largely based on formal logic.

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Magic square

In recreational mathematics and combinatorial design, a magic square is a n\times n square grid (where is the number of cells on each side) filled with distinct positive integers in the range 1,2,...,n^2 such that each cell contains a different integer and the sum of the integers in each row, column and diagonal is equal.

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Martin Richards (computer scientist)

Martin Richards (born 21 July 1940) is a British computer scientist known for his development of the BCPL programming language which is both part of early research into portable software, and the ancestor of the B programming language invented by Ken Thompson in early versions of Unix and which Dennis Ritchie in turn used as the basis of his widely used C programming language.

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Mathematical game

A mathematical game is a game whose rules, strategies, and outcomes are defined by clear mathematical parameters.

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Mathematical induction

Mathematical induction is a mathematical proof technique.

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Mathematical puzzle

Mathematical puzzles make up an integral part of recreational mathematics.

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Mathematician

A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

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Max Bezzel

Max Friedrich William Bezzel (4 February 1824 – 30 July 1871) was a German chess composer who created the eight queens puzzle in 1848.

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Millennium Prize Problems

The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000.

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Min-conflicts algorithm

In computer science, the min conflicts algorithm is a search algorithm or heuristic method to solve constraint satisfaction problems (CSP).

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Niklaus Wirth

Niklaus Emil Wirth (born 15 February 1934) is a Swiss computer scientist, best known for designing several programming languages, including Pascal, and for pioneering several classic topics in software engineering.

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No-three-in-line problem

In mathematics, in the area of discrete geometry, the no-three-in-line problem asks for the maximum number of points that can be placed in the n × n grid so that no three points are collinear.

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NP-completeness

In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.

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Ole-Johan Dahl

Ole-Johan Dahl (12 October 1931 – 29 June 2002) was a Norwegian computer scientist.

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Partial permutation

In combinatorial mathematics, a partial permutation, or sequence without repetition, on a finite set S is a bijection between two specified subsets of S. That is, it is defined by two subsets U and V of equal size, and a one-to-one mapping from U to V. Equivalently, it is a partial function on S that can be extended to a permutation.

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Pascal (programming language)

Pascal is an imperative and procedural programming language, which Niklaus Wirth designed in 1968–69 and published in 1970, as a small, efficient language intended to encourage good programming practices using structured programming and data structuring. It is named in honor of the French mathematician, philosopher and physicist Blaise Pascal. Pascal was developed on the pattern of the ALGOL 60 language. Wirth had already developed several improvements to this language as part of the ALGOL X proposals, but these were not accepted and Pascal was developed separately and released in 1970. A derivative known as Object Pascal designed for object-oriented programming was developed in 1985; this was used by Apple Computer and Borland in the late 1980s and later developed into Delphi on the Microsoft Windows platform. Extensions to the Pascal concepts led to the Pascal-like languages Modula-2 and Oberon.

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Permutation

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.

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Permutation matrix

\pi.

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Queen (chess)

The queen (♕,♛) is the most powerful piece in the game of chess, able to move any number of squares vertically, horizontally or diagonally.

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Recursion

Recursion occurs when a thing is defined in terms of itself or of its type.

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Rook (chess)

A rook (♖,♜) is a piece in the strategy board game of chess.

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Rook polynomial

In combinatorial mathematics, a rook polynomial is a generating polynomial of the number of ways to place non-attacking rooks on a board that looks like a checkerboard; that is, no two rooks may be in the same row or column.

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Search tree

In computer science, a search tree is a tree data structure used for locating specific keys from within a set.

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Sharp-P-complete

#P-complete, pronounced "sharp P complete" or "number P complete" is a complexity class in computational complexity theory.

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Structured programming

Structured programming is a programming paradigm aimed at improving the clarity, quality, and development time of a computer program by making extensive use of the structured control flow constructs of selection (if/then/else) and repetition (while and for), block structures, and subroutines in contrast to using simple tests and jumps such as the go to statement, which can lead to "spaghetti code" that is potentially difficult to follow and maintain.

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Sudoku

(originally called Number Place) is a logic-based, combinatorial number-placement puzzle.

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Symmetry

Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance.

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Tony Hoare

Sir Charles Antony Richard Hoare (born 11 January 1934), is a British computer scientist.

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Torus

In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

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W. W. Rouse Ball

Walter William Rouse Ball, known as W. W. Rouse Ball (14 August 1850 – 4 April 1925), was a British mathematician, lawyer, and fellow at Trinity College, Cambridge from 1878 to 1905.

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References

[1] https://en.wikipedia.org/wiki/Eight_queens_puzzle

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