Here's another way to do it:

#!/usr/bin/perl -w
use strict;

my @oldList = (1 .. 50);

my @newList =
  map { $_->[0] }
  sort { $a->[1] <=> $b->[1] }
  map { [$_, rand] } @oldList;

print "Numbers:\n", (join "-", @newList), "\n";
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Use the Schwartz, Luke!