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The eight queens puzzle is the problem of putting eight chess queens on an 8×8 chessboard such that none of them is able to capture any other using the standard chess queen's moves. (Piece colour is ignored, and any piece is assumed to be able to attack any other.) That is to say, no two queens should share the same row, column, or diagonal.
1 History
Over the years, many mathematicians, including Gauss have worked on this puzzle, which is a special case of the generalized problem of placing n "independent" queens on an n by n chessboard, posed as early as 1850 by Franz Nauck. In 1874, S. Gunther proposed a method of finding solutions by using determinants, and J.W.L. Glaisher refined this approach.
This puzzle was used in the popular early 1990s computer game, The 7th Guest.
2 Solutions
The eight queens problem has 92 distinct solutions, or 12 distinct solutions if symmetry operations such as rotations and reflections of the board are taken into consideration (via Burnside's lemma.)
3 Related problems
- Using pieces other than queens
- For example, on an 8×8 board one can place 32 independent knights, or 14 bishops, or 16 kings. Fairy chess pieces have also been substituted for queens.
- Nonstandard boards
- Polya studied the N-Queens problem on a toroidalSee also torus (nuclear physics). In geometry, a torus (pl. tori is a doughnut shaped surface of revolution generated by revolving a circle about an axis coplanar with the circle. The sphere is a special case of the torus obtained when the axis of rotatio ("donut-shaped") board. Other shapes, including three-dimensional "boards", have been studied.
- Domination
- Given an N×N board, find the domination number, which is the minimum number of queens (or other pieces) one needs in order to attack or occupy every square. For the 8×8 board, the queen's domination number is 5.
- Nine queens problem
- Place nine queens and one pawn on an 8×8 board in such a way that queens don't attack each other. Further generalization of the problem (solution is currently unknown): Given an N×N chess board and M>N queens, find the minimum number of pawns, so that queens and pawns can be set up on the board in such a way, that queens don't attack each other.
- magic squareIn mathematics, magic squares consist of a number of integers arranged in the form of a square in such a way that the sum of the numbers in every row, column and diagonal are the same. A magic square may have odd or even number of rows and columns. Usuall
- In 1992, Demirörs, Rafraf, and Tanik published a method for converting some magic squares into N-queens solutions, and vice versa.
- Latin squareA Latin square is an n × n table filled with n different symbols in such a way that each symbol occurs exactly once in each row and exactly once in each column. Here are two examples. Latin squares occur as the multiplication tables of a quasigroup. They
- Chess problemA chess problem is a puzzle set by somebody using chess pieces on a chess board, presenting the solver with a particular task to be achieved. For instance, a position might be given with the instruction that white is to move first, and checkmate black in
- Chess-type problemChess-type problems use the standard chess board or a variation of the standard chess board some or all of the chess pieces some or all of the chess rules However, chess-type problems may contain board setups that do not occur in an ordinary chess game.
