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steven0461 comments on Probability puzzles - Less Wrong
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A more general lesson is that whenever the answer to a puzzle causes you to go, "oh how wondrous that this question could have such a strange answer", you were probably tricked into accepting an anti-helpful framing of the problem, and one of the reasons why the puzzle-poser didn't guide you into a helpful framing instead was probably exactly that such anti-helpful framings cause people to feel that way.
Well, another general lesson. I think it's largely orthogonal to the general principle I mentioned. (For the avoidance of doubt, I agree with yours too.)
This post is not evidence for that lesson. When OP's puzzle is stated as intended it indeed has a wonderful and strange answer. The meta-puzzle: "Are these two puzzles essentially the same?" referring to the puzzle as intended and as presented also has a wonderful and strange answer; in fact, John Baez and maybe all of his commenters have been getting it wrong for several years. Our intuition is imperfect, and whether the puzzles you come across tend to use this fact or just trick you with sneaky framing depends on where you get your puzzles.