

The Problem

 100 prisoners are individually numbered 1 to 100
 A room having a cupboard of 100 opaque drawers numbered 1 to 100, that cannot be seen from outside.
 Cards numbered 1 to 100 are placed randomly, one to a drawer, and the drawers all closed; at the start.
 Prisoners start outside the room
 They can decide some strategy before any enter the room.
 Prisoners enter the room one by one, can open a drawer, inspect the card number in the drawer, then close the drawer.
 A prisoner can open no more than 50 drawers.
 A prisoner tries to find his own number.
 A prisoner finding his own number is then held apart from the others.
 If all 100 prisoners find their own numbers then they will all be pardoned. If any don't then all sentences stand. 


The task

 Simulate several thousand instances of the game where the prisoners randomly open drawers
 Simulate several thousand instances of the game where the prisoners use the optimal strategy mentioned in the Wikipedia article, of:
 First opening the drawer whose outside number is his prisoner number.
 If the card within has his number then he succeeds otherwise he opens the drawer with the same number as that of the revealed card. (until he opens his maximum).


Show and compare the computed probabilities of success for the two strategies, here, on this page.




References

 The unbelievable solution to the 100 prisoner puzzle standupmaths (Video).
 wp:100 prisoners problem
 100 Prisoners Escape Puzzle DataGenetics.
 Random permutation statistics#One hundred prisoners on Wikipedia.


/# Rosetta Code problem: http://rosettacode.org/wiki/100_prisoners
by Galileo, 05/2022 #/
 
include ..\Utilitys.pmt
 
def random rand * 1 + int enddef
 
def shuffle
    len var l
    l for var a
        l random var b
        b get var p
        a get b set
        p a set
    endfor
enddef
 
def play var optimal var iterations var prisoners
    0 var pardoned
 
    ( prisoners for endfor )
 
    iterations for drop
        shuffle
        prisoners for var prisoner
            false var found
            optimal if prisoner else prisoners random endif
            prisoners 2 / int for drop
                get dup prisoner == if true var found exitfor
                else
                    optimal not if drop prisoners random endif
                endif
            endfor
            found not if exitfor endif
            drop
        endfor
        pardoned found + var pardoned
    endfor
    drop
    pardoned 100 * iterations /
enddef
 
"Please, be patient ..." ?
 
( "Optimal: " 100 10000 true play
  " Random: " 100 10000 false play
  " Prisoners: " prisoners ) lprint