% 
% Dudeney's tea mixing problem in MiniZinc.
%
% From Martin Chlond Integer Programming Puzzles:
% http://www.chlond.demon.co.uk/puzzles/puzzles2.html, puzzle nr. 4.
% Description  : Dudeney's tea mixing problem
% Source       : Dudeney, H.E., (1917), Amusements in Mathematics, Thomas Nelson and Sons.

%
% This model was inspired by the XPress Mosel model created by Martin Chlond.
% http://www.chlond.demon.co.uk/puzzles/sol2s4.html

%
% Model created by Hakan Kjellerstrand, hakank@bonetmail.com
% See also my MiniZinc page: http://www.hakank.org/minizinc
%
int: tea = 3;

set of 1..tea: T = 1..tea;

array[T] of int: price;
array[T] of var int: x;
var int: minexp = sum(i in T) (x[i]*price[i]);  % total price

% minimize total prize
% solve minimize minexp;
solve :: int_search(x, "first_fail", "indomain", "complete") minimize minexp;

constraint
  forall(i in T) (x[i] >= 0)
  /\
  sum(i in T) (price[i]*x[i]) = 570 % 20 pound * 2s 4 1/2d = 20 * (24+4+1/2) = 570
  /\
  sum(i in T) (x[i]) = 20 % twenty pound

; 

price = [30, 27, 21];