Ah thanks :) But please bear with this nagging question: why doesn't \@letters point to the changed @letters inside the loop?

Update

Maybe I understand now...see modified code below:

use strict;

my $some_word = 'race';

my @letters = split //, $some_word;

my (@array1, @array2);

# Added this to show that the same $letter_ref is pushed into @array2

my $letters_ref = \@letters;

for (1..@letters) {
   my @new = @letters;
   push (@array1, \@new);
   push (@array2, $letters_ref);
   my $myshift = shift @letters;
   push(@letters, $myshift);
}
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Update 2

My above reasoning was wrong. See my reply to neniro at Re^2: Puzzled by array