% representation of the board
% col(.) and row(.) as in the queen example
% bad(.) for damaged cell
% ntiles is a constant for the number of tiles 
% report no answer in 58 sec

col(1..n).
row(1..n).

tile(1..ntiles). 

bad(1,1).
bad(3,3).

2 {cell(I,J,T) : col(I) : row(J) } 2 :- tile(T).

% bad cell needs not be covered 

:- col(I), row(J), tile(T), bad(I,J), cell(I,J,T).

% one tile over one cell only

:- col(I), row(J), tile(T1), tile(T2), neq(T1,T2),
   cell(I,J,T1), cell(I,J,T2).

% cell covered by the same tile must be neightbor
% (not far from each other)

:- tile(T), cell(I1,J1,T), cell(I2,J2,T), 
   col(I1), col(I2), 
   row(J1), row(J2), 
   I1 - I2 > 1.

:- tile(T), cell(I1,J1,T), cell(I2,J2,T), 
   col(I1), col(I2), 
   row(J1), row(J2), 
   J1 - J2 > 1.

% they cannot be on a diagonal

:- tile(T), cell(I1,J1,T), cell(I2,J2,T), 
   col(I1), col(I2), 
   row(J1), row(J2), 
   neq(I1,I2), neq(J1,J2).

hide row(_).
hide col(_).
hide tile(_).
hide bad(_,_).