#### The N Queens Problem

You have to place N queens on an N-by-N chessboard so that no two queens are on the same row, column or diagonal.

```check_determ
domains
int  = integer
ints = int*
predicates
nondeterm remove(int,ints,ints)
nonmember(int,ints)
integers(int,int,ints)
nondeterm queens(int,ints)
nondeterm queens_1(ints,int,ints,ints,ints,ints)
clauses

/* queens(N, Queens) is true if Queens is a placement that solves the N    */
/*   queens problem, represented as a permutation of the list of integers  */
/*   [1, 2, ..., N].                                                       */
queens(N, Queens):-
N > 0,
integers(1, N, Rows),
queens_1(Rows, N, [], [], [], Queens).

queens_1([], 0, Queens, _, _, Queens).
queens_1(Rows, Col, A, B, C, Queens):-
remove(Row, Rows, Rows1),
/* All squares on the same NW-SE diagonal have the same value of Row+Col */
RowPlusCol  = Row + Col, nonmember(RowPlusCol,  B),
/* All squares on the same SW-NE diagonal have the same value of Row-Col */
RowMinusCol = Row - Col, nonmember(RowMinusCol, C),
Col1 = Col - 1,
queens_1(Rows1, Col1, [Row|A], [RowPlusCol|B], [RowMinusCol|C], Queens).

/* integers(M, N, Is) is true if Is is the list of integers from M to N    */
/*   inclusive.                                                            */
integers(N, N, [N]):-!.
integers(I, N, [I|Is]):-I < N, I1 = I + 1, integers(I1, N, Is).

/* remove(X, Ys, Zs) is true if Zs is the result of removing one           */
/*   occurrence of the element X from the list Ys.                         */
remove(X, [X|Ys], Ys).
remove(X, [Y|Ys], [Y|Zs]):-remove(X, Ys, Zs).

/* nonmember(X, Xs) is true if X is not a member of the list Xs.           */
nonmember(X, [Y|Ys]):-X <> Y, nonmember(X, Ys).
nonmember(_, []).
```