The solution you came up with on your own WAS through logic, not trial-and-error. Others will correct me if I'm wrong (and even if I'm not), but your approach is generally the most effective one to take when solving this type of puzzle. Look for a place to enter the puzzle - like a line with 3 correct answers - and deduce from there.
For another Mastermind-style challenge, you may want to check out
http://www.PuzzleMonster.com/horoscope.asp . It's a personalized horoscope, but to get to it you have to figure out the passcode, which, like the horoscope, changes daily.
-Puzzle Monster