% 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 

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

tile(1..ntiles). 

bad(1,1).
bad(3,2).

1 {cell(I,J,T) : tile(T) } 1 :- col(I), row(J), not bad(I,J).

% constraint checking

% one tiles cannot cover more than two cells

:- tile(T), cell(I1,J1,T), cell(I2,J2,T), cell(I3,J3,T),  
   col(I1), col(I2), col(I3),
   row(J1), row(J2), row(J3),
   I1 > I2, I2 > I3.
   
:- tile(T), cell(I1,J1,T), cell(I2,J2,T), cell(I3,J3,T),  
   col(I1), col(I2), col(I3),
   row(J1), row(J2), row(J3),
   I1 = I2, J1 > J2, I2 > I3.

:- tile(T), cell(I1,J1,T), cell(I2,J2,T), cell(I3,J3,T),  
   col(I1), col(I2), col(I3),
   row(J1), row(J2), row(J3),
   I1 = I2, J1 > J2, I3 > I2.

:- tile(T), cell(I1,J1,T), cell(I2,J2,T), cell(I3,J3,T),  
   col(I1), col(I2), col(I3),
   row(J1), row(J2), row(J3),
   I1 = I2, I2 = I3, J1 > J2, J2 > J3.
 
% one tile cannot cover only one cell 
% do we need it (?)

% 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(_,_).