set(arithmetic).

% KenKen is a puzzle similar in some ways to Sudoku.
% Solutions are Latin squares (each row and each column
% is a permuatation of the domain).  The grid is partitioned
% into blocks of various sizes and shapes, and an arithmetic
% relation is specified for each block; for example, the
% sum of the members is 8, or the difference (for a block of
% size 2) is 3.
%
% See the Wikipedia Web page on KenKen.
%
% Ordinarily, KenKen uses {1,...,n}, but we use {0,...,n-1}.

assign(domain_size, 6).  % domain is {0,1,2,3,4,5}
assign(max_models, -1).  % find all models

formulas(assumptions).

% Latin Square

 f(x,y1) = f(x,y2) -> y1=y2.
 f(x1,y) = f(x2,y) -> x1=x2.

% Clues for the blocks.

 f(0,1) * f(0,2) = 0.
 f(0,0) + f(1,0) = 5.
 f(0,3) * f(1,3) = 20.
 f(0,4) * f(0,5) * f(1,5) * f(2,5) = 6.
 f(1,4) + f(2,4) = 2.
 abs(f(1,1) + -f(1,2)) = 3.
 f(2,0) * f(2,1) * f(3,0) * f(3,1) = 240.
 f(2,2) * f(2,3) = 6.
 f(3,2) * f(4,2) = 0.
 f(3,3) + f(4,3) + f(4,4) = 7.
 f(3,4) * f(3,5) = 0.
 f(4,0) * f(4,1) = 6.
 abs(f(4,5) + -f(5,5)) = 1.
 f(5,0) + f(5,1) + f(5,2) = 8.
 f(5,3) + f(5,4) = 3.

end_of_list.