sub checker
{
   my ($str) = @_;
   for ('00' .. '99')
   {
      my $n = 0;
      $n++ while $str =~ /$_/g;
      die "'$_' appears $n times\n" if $n != 1;
   }
}
 
sub generate
{
 0         1         2         3         4         5         6        
+ 7         8     
#012345678901234567890123456789012345678901234567890123456789012345678
+90123456789012345
 for$x(0..9){for$y(0..9){/$x$y/||(/^$y/and$_="$x$_")||(/$x$/and$_.=$y)
+or$_.="$x$y"}}$_ 
}
 
print "Generating ...\n";
my $test = generate();
print "$test\n";
 
print "Checking   ...\n";
checker($test);
 
print "Ok\n";
----
Generating ...
9900102030405060708091121314151617181922324252627282933435363738394454
+6474849556575859667686977879889
Checking   ...
Ok
[download]

I know it can be improved ...

Update: 78 chars and counting ...

#0         1         2         3         4         5         6        
+ 7         8
#012345678901234567890123456789012345678901234567890123456789012345678
+901234567890
 for$x(0..9){for$y(0..9){/$x$y/||(/^$y/?$_=$x.$_:(/$x$/?$_.=$y:($_.=$x
+.$y)))}}$_
[download]

Update: 72 chars and counting ...

#0         1         2         3         4         5         6        
+ 7
#012345678901234567890123456789012345678901234567890123456789012345678
+9012345
 for$x(0..9){for$y(0..9){/$x$y/||($_=/^$y/?$x.$_:/$x$/?$_.$y:$_.$x.$y)
+}}$_
 for$x(0..9){for$y(0..9){$_=/$x$y/?$_:/^$y/?$x.$_:/$x$/?$_.$y:$_.$x.$y
+}}$_
[download]

------
We are the carpenters and bricklayers of the Information Age.

The idea is a little like C++ templates, except not quite so brain-meltingly complicated. -- TheDamian, Exegesis 6

Please remember that I'm crufty and crochety. All opinions are purely mine and all code is untested, unless otherwise specified.