/* 

  Werewolfes II (Smullyan) puzzle in Picat.

  From Martin Chlond Integer Programming Puzzles:
  http://www.chlond.demon.co.uk/puzzles/puzzles3.html, puzzle nr. 9.
  Description  : Werewolves II
  Source       : Smullyan, R., (1978), What is the Name of this Book?, Prentice-Hall

  This model was inspired by the XPress Mosel model created by Martin Chlond.
  http://www.chlond.demon.co.uk/puzzles/sol3s9.html


  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 =>
  Person = 3,
  X = new_list(Person), % x(i) = 1 if person i is a knight, 0 if a knave
  X :: 0..1,

  Y = new_list(Person), % y(i) = 1 if person i is a werewolf, 0 otherwise
  Y :: 0..1,

  Z #= sum([X[I]+9*X[3] : I in 1..Person]),

  % only one is a werewolf
  sum(Y) #= 1,

  % if statement 1 is true then set x(1) = 1, else 0
  Y[1] - 9*X[1] #<= 0,
  Y[1] - X[1] #>= 0,

  % if statement 2 is true then set x(2) = 1, else 0
  Y[2] - 9*X[2] #<= 0,
  Y[2] - X[2] #>= 0,

  % if statement 3 is true then set x(3) = 1, else 0
  sum([X[I]+9*X[3] : I in 1..Person]) #>= 2,
  sum([X[I]+9*X[3] : I in 1..Person]) #<= 28,

  Vars = X ++ Y ++ [Z],
  solve(Vars),
  println(z=Z),
  println(x=X),
  println(y=Y),
  nl,
  fail,
  
  nl.
go => true.