

Solve the eight queens puzzle.



You can extend the problem to solve the puzzle with a board of size   NxN.

For the number of solutions for small values of   N,   see   OEIS: A000170.



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safe[q_List, n_] := 
 With[{l = Length@q}, 
  Length@Union@q == Length@Union[q + Range@l] == 
   Length@Union[q - Range@l] == l]
nQueen[q_List: {}, n_] := 
 If[safe[q, n], 
  If[Length[q] == n, {q}, 
   Cases[nQueen[Append[q, #], n] & /@ Range[n], 
    Except[{Null} | {}], {2}]], Null]