/* envlet.tc - tct - 3/22/9

/* 10 addressed envelopes, 10 addressed letters randomly stuffed in them. 
/* what's average number of correctly stuffed letters?

/* can be shown answer is 1 (in fact, n envelopes, n letters, for any n, gives
/* 1 on average). this simulates the situation.

dpf int n,d,p [
 /* display proper fraction n/d as decimal number
 /* with p digit precision 
 int w
 w=10*n/d
 if (p) [
  MC w,14
  dpf 10*n%d,d,p-1 /* recursive call
  ]
 ]

int last

rand [ /* returns random number in 1..2^31-1
 int m;m=2147483647
 int a;a=16807	
 last=last*a%m
 if (last<0) last=-last
 return last
 ]	

/* this was motivated by DeeDee's post
/* http://tobee-interpres.blogspot.com/2009/03/more-stats.html

envlet [
 pl "";ps "envlet.tc - 3/22/9 - tct";pl "";pl ""
 ps "seed (e.g. 315) ";last=gn;if (last%2==0) ++last /* make odd
 pl "number of simulations (e.g. 1, 100, 200, 2000, 15000 etc.) "
 int ul;ul=gn
 int i,j,a(10),c,r,d,matched,sm,b(10)
 for (j=1;j<=ul;++j) [
  for (i=1;i<=10;++i) a(i)=0
  c=0
  while (c<10) [
   r=(rand()+1)/2%10+1 /* r is in 1..10
   d=1
   while ((a(d)!=r)*(d<=c)) ++d
   if (d>c) a(++c)=r
   ]
  sm=matched /* save matched 
  for (i=1;i<=10;++i) if (a(i)==i) ++matched
  ++b(matched-sm)
  ]
 pl "on average,";pn matched/ul;ps "."
 dpf matched%ul,ul,4;ps " onvellopes wur korrektlee stuffid.";pl ""
 pl "total onvellopes korrektlee stuffid: ";pn matched;pl ""
 for (i=0;i<=10;++i) [
  pl "";ps "There were";pn b(i);ps " cases of";pn i;ps " korrektlee stuffid onvellopes."
  ] 
 pl ""
 ]