/* 

  Water glass riddle in Picat.

  From MindYourDecisions
  Can you solve the water glass and wine bottle riddles?
  https://www.youtube.com/watch?v=ex7ag9U-dzU
  """
    [5 stacked glasses: 34 cm
     2 stacked glasses: 19 cm
     1 glass          :  ? 
    ]

    How tall is one glass?
  """

  Answer: One glass is 14cm.

  The non-hidden part is 5cm.

  Mathematica:
  In[1]:= Solve[{(x+y*4)==34,(x+y*1)==19}]
  Out[1]= {{x -> 14, y -> 5}}


  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import cp.
% import mip. % Checking for a float solutions (go2/0)

main => go.

go ?=>
  X :: 1..30, % The base of the glass
  Y :: 1..30, % The rest of the glass, i.e. the part that's not hidden in the stack.

  (X + 4*Y) #= 34,
  (X + 1*Y) #= 19,

  solve($[cbc],[X,Y]),
  println([x=X,y=Y]),
  fail,

  nl.
go => true.

% Checking float version.
% Same (integer) solution: 14cm and 5cm
go2 ?=>
  X :: 1.0..30.0, % The base of the glass
  Y :: 1.0..30.0, % The rest of the glass, i.e. the part that's not hidden in the stack.

  (X + 4*Y) #= 34.0,
  (X + 1*Y) #= 19.0,

  solve($[glpk],[X,Y]),
  println([x=X,y=Y]),
  fail,

  nl.
go2 => true.