/* 

  Dice problem in Picat.

  From Gamble's example dice.rkt
  """
  Somebody gives Norman a hat containing five slips of paper, numbered 1
  to 5 respectively. Norman draws a slip from the hat. The number on the
  slip is called n. Norman then repeats the following procedure ten
  times:

  Take n dice from the bag, throw them, report the total t, then put the
  dice back in the bag.

  The totals reported are 21, 15, 34, 12, 18, 38, 46, 13, 24, and 27.

  The question is, what is the number on the slip Norman drew? (That is,
  what is n?)

  Assume all of the dice in the bag are 20-sided.
  """


  The result (for the accepted n) should be something like this (from my Gamble model)
  3: 0.9999365920526166
  4: 6.340794738337384e-5
  5: 8.187980010948882e-34
  mean: 3.0000634079473834

  This is a port of my Racket/Gamble model dice.rkt

  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.

main => go.


/*
 
  min_accepted_samples = 1000
  var : n
  Probabilities:
  3: 0.99800000000000000 (499 / 500)
  4: 0.00200000000000000 (1 / 500)
  mean = 3.002

*/ 
go ?=>
  reset_store,
  run_model(1_000_000,$model,[show_probs_rat,mean,
                              min_accepted_samples=1000 % ,show_accepted_samples=true
                              ]),
  % show_store_lengths,nl,
  nl.
go => true.

/*

  The 'trickery' is to find the smallest possible n by notice that 46 implies 
  that n must be at least 46/20 = 2.3, i.e. at least n = 3.

*/
model() =>
  Totals = [21,15,34,12,18,38,46,13,24,27],  
  Len = Totals.len,
  
  % The minimum number of N that's possible is 3 (see comment above)
  MinN = ceiling(Totals.max / 20), 
  N = MinN + random_integer(5-MinN),

  S = [ [dice(20) : _ in 1..N].sum : _ in 1..Len],
  observe_abc(Totals,S,1/2),
  
  if observed_ok then
    add("n",N)
  end.