/* 

  Average prime numbers puzzle in Picat.

  From Chris Smith's Math letter #674
  """
  Find me three different two-digit prime numbers so that:
  - the average of any pair of these prime numbers is a prime number
  - the average of all three primes is also a prime number
  """

  Unique solution:
  [11,47,71]

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

*/

import util.
import cp.

main => go.

go ?=>
  N = 3,
  Primes = [I : I in 10..99,prime(I)],

  X = new_list(N),
  X :: Primes,
  
  all_different(X),
  increasing(X), % symmetry breaking

  % the average of any pair of these prime numbers is a prime number
  foreach(I in 1..N, J in I+1..N)
    T :: Primes,
    2*T #= X[I]+X[J]
  end,
  % the average of all three primes is also a prime number  
  S :: Primes,  
  3*S #= sum(X),

  solve(X),
  println(X),
  fail,
  nl.
go => true.