Very interesting game! I was clicking random doors by the end but it was fun. Great job!
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That's also a strategy! As I said, hints are there for you not having to loop around in circles. "they can save you iterations."
The game's called Next Iteration because you go around in a loop, and then click the door you didn't click earlier, and maybe that'll lead you to the answer, it's like iterating through items in a for-loop.