The cheat code is recognition.
You know something from already having been exposed to it, and by recognizing it. The mechanism is effortless (as KISS as you can get). Pattern is matched to pattern without the help of anything demanding the exercise of free will and/or choosing. You encounter something, the digits of pi or the lyrics of a song for example, and you know what you are looking at. If you did not recognize them you'd be without much hope of first generating them to then recognize with them.
With as few as 5 words in an expression you can guess the 6th with impressive accuracy. Cognition can be faked this way by a LLM. With enough recognition, a poem-puzzle can be solved without much effort.
JP seems to have understood this, as he went looking to recognize facial expressions as a way to avoid thinking about things at all. We can possibly recognize he is at this again by using other silent means of communication. If we do it's an effortless gain.
The best thing about this sort of mechanism is the solve can select for you. It's very humbling, because the solver ends up being like a slumdog millionaire just facing things he recognizes. He comes out looking like a genius. And, of course, you'd be accused of cheating.
Success comes from preparedness. It is very much like a lottery ticket containing a multi-digit combination. The hope is that there's a ticket out there with this solve' s combination on it. As JP gives out hints the match becomes more likely to express itself if we recognize the clue.