N-queens Puzzle

<p>The&nbsp;<b >eight queens puzzle</b>&nbsp;is the problem of placing eight&nbsp;<a href="http://en.wikipedia.org/wiki/Chess" title="Chess" >chess</a>&nbsp;<a href="http://en.wikipedia.org/wiki/Queen_(chess)" title="Queen (chess)" >queens</a>&nbsp;on an 8×8 chessboard so that no two queens attack 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&nbsp;<b ><i>n</i>-queens problem</b>&nbsp;of placing&nbsp;<i >n</i>&nbsp;queens on an&nbsp;<i >n</i>×<i >n</i>&nbsp;chessboard, where solutions exist for all natural numbers&nbsp;<i >n</i>&nbsp;with the exception of 2 and 3.<sup id="cite_ref-0" class="reference" ><a href="http://en.wikipedia.org/wiki/Eight_queens_puzzle#cite_note-0" >[1]</a></sup>

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<img src="/448e313a-34a7-5e06-8833-c16c52b2babd.png"/></p>