/* 

  McNuggets Problem (Rosetta Code) in Picat.

  http://rosettacode.org/wiki/McNuggets_Problem#MiniZinc
  """
  From Wikipedia:
  '''
  The McNuggets version of the coin problem was introduced by Henri Picciotto,
  who included it in his algebra textbook co-authored with Anita Wah. Picciotto
  thought of the application in the 1980s while dining with his son at
  McDonald's, working the problem out on a napkin. A McNugget number is
  the total number of McDonald's Chicken McNuggets in any number of boxes.
  In the United Kingdom, the original boxes (prior to the introduction of
  the Happy Meal-sized nugget boxes) were of 6, 9, and 20 nuggets.
  '''

  Task

  Calculate (from 0 up to a limit of 100) the largest non-McNuggets number (a number n 
  which cannot be expressed with 6x + 9y + 20z = n where x, y and z are natural numbers). 
  """

  Also see: http://hakank.org/picat/frobenius_number.pi


  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 =>
  N :: 0..100,
  foreach(X in 0..16, Y in 0..11, Z in 0..5)
     6*X + 9*Y + 20*Z #!= N
  end,
  solve($[max(N)],N),
  println(n=N),
  nl.


go2 =>
  T = [N : N in 1..100,
            member(X,0..16), member(Y,0..11), member(Z,0..5), 6*X + 9*Y + 20*Z != N],
  println(t=T),
  println(max=Max),
  nl.