Aside: Just for fun, I tried the puzzle in ChatGPT. Apparently there’s a limited number of responses allowed in the high-end model, before it bumps you down to a weaker model. The first eight questions it asked were pretty good (including some nobody here has asked yet), but after that it started asking redundant questions.
Also, it summarized its current knowledge after every question, sometimes a short summary, and sometimes a longer one. I think this was mostly to “remind itself”, to keep it in the context window, but its short summaries still managed to keep the most relevant information.
It also padded a lot with “That’s really interesting!” and the like. After 34 questions, it started just giving me a summary of what it knew so far, and insisted that that was the solution. I had to keep telling it that it needed to be more specific, and then tell it to go back to trying yes-no questions.
Eventually, after 56 questions, it (mostly) got it.