/* 

  100 students problem in Picat.

  From https://twitter.com/mathisstillfun/status/1588002151804157952
  """
  100 students take an exam with 4 questions. 90 solve the first question, 
  85 the second, 80 the third, and 70 the fourth. Determine the smallest possible
  number of students that have solved all four questions
  """

  Solution: 25 students

  MIP: cbc: 0.152s glpk: 0.118s
  All the other solvers are way too slow on this.

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

*/

import mip.
% import smt.
% import sat.
% import cp.

main => go.

go =>
  N = 100,
  M = 4,

  X = new_array(M,N),
  X :: 0..1,

  sum(X[1]) #= 90,
  sum(X[2]) #= 85,
  sum(X[3]) #= 80,
  sum(X[4]) #= 70,

  Z #= sum([ sum([X[I,J] : I in 1..M]) #= M : J in 1..N ]),
  
  solve($[min(Z),inout,updown,report(printf("z:%d\n",Z))],X.vars),
  println(z=Z),
  flush(stdout),
  fail,
  
  nl.