/* 

  Mr Shearer's class in Picat.

  From https://minerva-demo.github.io/#category=Probability&index=2
  """
  Question
  Three-fourths of the students in Mr. Shearer's class have brown hair and 
  six-sevenths of his students are right-handed. If Mr. Shearer's class has 
  28 students, what is the smallest possible number of students 
  that could be both right-handed and have brown hair?
  ...

  Reference answer
  Mr. Shearer has 3/4(28)=21 students with brown hair and 6/7(28)=24 students 
  who are right-handed. Since there are 28-24=4 left-handed students, at most 4 
  of the 21 brown-haired students are left-handed. Therefore, at least 17 of 
  them are right-handed. Final Answer: The final answer is 17.
  ...
  Problem source: MATH Counting & Probability Level 1
  """

  Cf my WebPPL model http://hakank.org/webppl/mr_shearers_class.wppl

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

*/

% import sat. % 1.0s
% import cp. % too slow
import mip. % GLPK: 0.18ss Cbc: 0.2
% import smt. % > 30min

main => go.

go =>
  nolog,
  NumStudents = 28,
  
  % 3/4 of the class has brown hair
  HasBrownHair = new_list(NumStudents),
  HasBrownHair :: 0..1,
  sum(HasBrownHair)*4 #=3*NumStudents,

  % 6/7 of the class is right handed
  IsRightHanded = new_list(NumStudents),
  IsRightHanded :: 0..1,
  sum(IsRightHanded)*7 #= 6*NumStudents,

  % How many has both brown hair and are right handed?
  NumBoth #= sum([HasBrownHair[I]*IsRightHanded[I] #= 1 : I in 1..NumStudents ]),

  Vars = HasBrownHair ++ IsRightHanded,
  solve($[glpk,min(NumBoth),degree,down,report(printf("num_both:%d\n",NumBoth))],Vars),
  println(numBoth=NumBoth),
  
  nl.