/* 

  Invisible dice in Picat.

  From https://brainstellar.com/puzzles/probability/24
  """
  Invisible Dice

  I bought two fair six-sided dice. Keeping the first one untouched, I modified 
  the second die, by erasing each face and writing a number of my own. Now, the sum of 
  outcomes of the two dice is equally likely an integer between 1 and 12. Can you 
  deduce the numbers written on the modified die?

  Note: For each dice, each face is equally likely to turn up after a toss.
  """

  Cf my CP model invisible_dice.pi

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

*/

import ppl_distributions, ppl_utils.
import util.
% import ordset.

main => go.

/*

  Num accepted samples: 10  Total samples: 16534  (0.001%)

  var : die2
  Probabilities:
  [0,0,0,6,6,6]: 1.0000000000000000

  var : sums
  Probabilities:
  [1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9,10,10,10,11,11,11,12,12,12]: 1.0000000000000000

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs, % mean,
                           % show_percentiles,show_histogram,
                           % show_hpd_intervals,hpd_intervals=[0.94],
                           min_accepted_samples=10,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  


model() =>
  Die1 = 1..6,

  % Generate 6 random number from 0..6
  Die2 = random_integer_n(7,6).sort,

  % Get all possible combinations (and sort them)
  Sums = [ D1+D2 : D1 in Die1, D2 in Die2].sort,
  Freq = Sums.get_freq, % Get their frequencies

  % Each sum 2..12 should have exactly 36/12 = 3 occurrences
  foreach(I in 1..12)
    observe(Freq.get(I,0) == 3)
  end,
  
  if observed_ok then
    add("die2",Die2),
    add("sums",Sums),    
  end.