Here's my round 1 solution. Fancier solutions to come, work willing.

while (<DATA>) {
    chomp;
    my $line = $_;
    my @chars = split '';
    my $diff = join '', map {($chars[$_+1] - $chars[$_]) % 10} (0..$#c
+hars-1);

    my $maxlen = 0;
    my $maxpos = 0;
    while ($diff =~ m/(1+|9+)/g) {
        if ($maxlen < length $1) {
            $maxlen = length $1;
            $maxpos = pos($diff) - $maxlen;
        }
    }
    printf "pos = % 2s, str = '%s'\n", $maxpos, substr($line, $maxpos,
+ $maxlen + 1);
}
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