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But this makes no sense. You're proving the "counterintuitive answer" with the probability theory but when confronted with the fact that your proof is not mathematically correct you say "this is a simple brain teaser"The answer IS mathematically correct. It's just counterintuitive and it made some PhDs trip.
Nobody here -- not even you, before -- was arguing it's mathematically incorrect. Some people, when told the right answer, claimed the problem is underspecified and admits more than one context that may change the answer, which is not at all the same as saying the answer is mathematically incorrect! Not even Diaconis, the person some of you are so eager to defend (for some bizarre reason) claims it's "mathematically incorrect"!
It seems you're grasping at straws now.