Wired Cola

...that 5 of Andrew's 212 friends share a birthday.

#!/usr/bin/perl

#monte carlo calculation on Andrew's Birthday question.
# In short, this code allows a general test of the question:
# "if I have x friends, what are the chances that any y of
# them share a birthday?" It does so using Monte Carlo technique.
# runs should be set high (at least 1000, maybe higher) to give a
# good answer. I don't know what gives good confidence here.

# init a few things. bdaymatches is how many friends share one birthday.
use constant friends => 212;
use constant runs => 10000;
use constant bdaymatches => 5;
$foundmatches = 0;

# this loop calls yeartally once per run, adding each run to the array of
# runs called fullrun.
for ($i = 1; $i <= runs; $i++)
{
@temp = &yeartally;
$fullrun[$i] = [ @temp ];
#print "@temp\n";
# printf "THIS IS A YEAR BREAK \n";
}
#debug printing of the array:
# for $aref ( @fullrun) { print "\t [ @$aref ], \n"; }
for ($j=1; $j <= runs ; $j++ ) {
for ($k=0; $k <= 365 ; $k++) {
#print "$j, $k, $fullrun[$j][$k]";
if ($fullrun[$j][$k] >= bdaymatches) {
# print "incrementing...";
$foundmatches++;
}
}
}
#we really want matches/year
$foundmatches = $foundmatches / runs;
print "approx p for this formula: $foundmatches\n";
print "end of run";
# returns an array of counts of the number of people sharing each
# day of the year as a birthday.

sub yeartally()
#this is a sub because I thought that would save me zeroing things. Nope.
{
my @oneyear = ();
for ($j = 1; $j <= friends; $j++)
{
$x = int(365*rand);
$oneyear[$x]++;
# printf "%d \n", $x;
}
# print "@oneyear\n";
return @oneyear;
}