First you make a copy of @letters:

   my @new = @letters;
[download]

Then you change @letters directly:

   my $myshift = shift @letters;
   push(@letters, $myshift);
[download]

But you never change the copy. Why would you expect it to be changed?

Update: ugh, Tanktalus is right. I didn't read the code carefully enough. Please read his reply instead. :-)