%% representing the board
%% using n as a constant 

col(1..n).   % n column
row(1..n).   % n row

%% generating the solution.

1 {cell(I,J) : row(J)} 1:- col(I).   % each column one queen

% two queens cannot be on the same row

%:- col(I), row(J1), row(J2), neq(J1,J2), cell(I,J1), cell(I,J2).

% two queens cannot be on the same column

:- row(J), col(I1), col(I2), neq(I1,I2), cell(I1,J), cell(I2,J).

% two quuens cannot be on a diagonal

:- row(J1), row(J2), J1 > J2,
   col(I1), col(I2), I1 > I2, 
   cell(I1,J1), cell(I2,J2), 
   eq(I1 - I2, J1 - J2).

:- row(J1), row(J2), J1 > J2,
   col(I1), col(I2), I1 < I2, 
   cell(I1,J1), cell(I2,J2), 
   eq(I2 - I1, J1 - J2).

% hiding 'unneccessary' atoms

hide row(_).
hide col(_).