The regex is anchored to the beginning of the string. The first assertion is a positive look-ahead that says "see if we can find zero or more digits, followed by a particular digit, followed by zero or more digits, and then that particular digit again". That satisfies the "at least one digit must be duplicated" rule. The second assertion is a negative look-ahead that says "make sure we can't match zero or more digits, that particular digit, zero or more digits, that particular digit, and then zero or more digits and that particular digit a THIRD time". This satisfies the "the digit can't appear more than three times" rule.
Jeff japhy Pinyan, P.L., P.M., P.O.D, X.S.: Perl, regex, and perl hacker
How can we ever be the sold short or the cheated, we who for every service have long ago been overpaid? ~~ Meister Eckhart

In reply to Re^3: Find duplicate digits by japhy
in thread Find duplicate digits by Anonymous Monk

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