/* 

  Find the triangle in Picat.

  From Adrian Groza "Modelling Puzzles in First Order Logic"
  """
  Puzzle 17. Find the triangle

  The sides and height of a triangle are four consecutive whole numbers. What is the
  area of the triangle? (puzzle 230 from Dudeney (2016))
  """

  Solution
  [h = 12,a = 13,b = 14,c = 15,area = 84]

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

*/

import cp.

main => go.

go ?=>
  % A, B, and C are the sides, S is the height
  X = [H,A,B,C,Area],
  X :: 1..100,
  
  A + 1 #= B,
  B + 1 #= C,
  H+1 #= A #\/ C + 1 #= H,

  2*Area #= A*H #\/ 2*Area #= B*H #\/ 2*Area #= C*H,

  2* P #= A+B+C,
  Area*Area #= P*(P-A)*(P-B)*(P-C),

  solve(X),
  println([h=H,a=A,b=B,c=C,area=Area]),
  fail,
  
  nl.
go => true.