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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. Thus, a solution requires that no two queens share the same row, column, or diagonal. The eight queens puzzle is an example of the more general ''n''-queens problem of placing ''n'' queens on an ''n''×''n'' chessboard, where solutions exist for all natural numbers ''n'' with the exception of ''n''=2 and ''n''=3.〔Hoffman, et al. "Construction for the Solutions of the m Queens Problem". Mathematics Magazine, Vol. XX (1969), p. 66–72. ()〕
==History==
Chess composer Max Bezzel published the eight queens puzzle in 1848. Franz Nauck published the first solutions in 1850.〔W. W. Rouse Ball (1960) ''The Eight Queens Problem'', in Mathematical Recreations and Essays, Macmillan, New York, pp 165-171.〕 Nauck also extended the puzzle to the ''n''-queens problem, with ''n'' queens on a chessboard of ''n'' × ''n'' squares.
Since then, many mathematicians, including Carl Friedrich Gauss, have worked on both the eight queens puzzle and its generalized ''n''-queens version. In 1874, S. Gunther proposed a method using determinants to find solutions.〔 J.W.L. Glaisher refined Gunther's approach.
In 1972 Edsger Dijkstra used this problem to illustrate the power of what he called structured programming. He published a highly detailed description of a depth-first backtracking algorithm.2
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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