32:my $only_unique = 1;    # eliminate numbers that are just a reorder
+ing of digits

43:    ## we store only unique "constellations" of digits by sorting a
+nd using the
44:    ## hash to remove duplicates. we also must sort the value it po
+ints to.
45:    if ($only_unique) {$n = sortHiLow($n);
46:                       $nn = sortHiLow($nn);}
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You only use $only_unique in one place and you never change its value.

100:## runs kaprekar routine on a number until it either cycles or con
+verges:
101:sub kRoutine {
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You never call this subroutine from anywhere so why is it here?

72:## given a number, performs one iteration of the kaprekar routine a
+nd returns num
73:sub gotoNext {
74:    my $n = shift;
75:    my $new_num = sortHiLow($n) - sortLowHi($n); 
76:    while (length $new_num < $digits) 
77:        {$new_num = ("0" . "$new_num")}
78:        
79:    return $new_num;
80:}
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You can use sprintf to pad a number with leading zeros:

sub gotoNext {
    my $n = shift;
    sprintf '%0*d', $digits, sortHiLow( $n ) - sortLowHi( $n );
}
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