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$size[$_] = @{ $list[ $_ ] } for 1..$phrase_length;

Can't use an undefined value as an ARRAY reference at anagram.pl line 
+34.

for my $length ( 1..$phrase_length )
{
...
    $size[$length] 
          = ( $ref =~ /ARRAY/ ? @{ $list[ $length ] } : 0 );
}