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my $alphabetised = "1";                # Sets $alphabetised to "1"

...
                                       # TRUE before we even begin
                                       # Thus, never executed
};

until ($alphabetised == "1"){          # Checks instead of sets
until ($alphabetised eq "1"){          # Checks instead of sets
while ($alphabetised eq "1"){          # while() instead of until()
my $alphabetised = "0";                # Initialize differently