Fun problem, here's a suggestion and a solution.

Your algorithm doesn't work very well if the desired average is near your minimum or maximum, like from 0 - 100, desired average = 10.

If you want random numbers from $start to $end, instead of $number = rand($end) and testing to see if it's bigger than $start, use $number = rand($end - $start) + $start.

This program will either choose a random number from $start to $average or from $average to $end, based on whether the actual average is lesser or greater than the target average.

I have no idea what the distribution will look like, or what you want the distribution to look like.

YuckFoo

#!/usr/bin/perl

   use strict;

   my ($MIN, $MAX, $NUM, $AVERAGE) = qw(0 100 64 32);

   my $small = $AVERAGE - $MIN;
   my $large = $MAX - $AVERAGE;

   my ($i, $rand, $total, $actual);

   for ($i = 1; $i <= $NUM; $i++) {

      if ($actual < $AVERAGE) {
         $rand = int(rand($large) + $AVERAGE);
      }
      else {
         $rand = int(rand($small) + $MIN);
      }

      $total += $rand;
      $actual = $total / $i;

      print "$rand $actual\n";
   }
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