/* 

  Four rectangle problem in Picat.

  https://mindyourdecisions.com/blog/2017/12/20/can-you-solve-the-rectangle-area-puzzle/
  """
  A large rectangle is divided into four rectangles, three of which have areas 16, 13, and 39 as 
  drawn in the following figure:
     
   [
             x        len
        --------------
        | 13 |  39   | 
        --------------  y
        | 16 |   ?   |      
        -------------- height
    
   ]

  What is the area of the fourth rectangle
  """


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

*/

import cp.


main => go.

go ?=>
  L = [Area1,Area2,Area3,Area4,Len,Height,X,Y],
  L :: 1..100,

  Area1 #= 13,
  Area2 #= 39,
  Area3 #= 16,
  X*Y #= Area1,
  (Len-X)*Y #= Area2,
  (Height-Y)*X #= Area3,
  (Height-Y)*(Len-X) #= Area4,
  (Len*Height) #= Area1+Area2+Area3+Area4,


  solve(L),

  println(area4=Area4),
  println([area1=Area1,area2=Area2,area3=Area3,area4=Area4,len=Len,height=Height,x=X,y=Y]),
  fail,
  
  nl.

go => true.