Rather than using a shortcut to find various possible combinations of, jude systematically lists every possible combination to determine the correct code. jude is solving his problem by the use of

... brute force. Suppose you know a certain password has exactly 5 uppercase letters, you could hack it by simply trying 26x26x26x26x26 combinations. Practically, security systems should be designed in such a way that a brute-force attack is useless (ie., it would take millions of years)

Poor Jude though.