Shamelessly stolen from you-know-where.
this post was submitted on 25 Jun 2025
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When Albert says he knows Bernard doesn't know, he is saying that in Albert's row, every single ball has a ball below/above it. This eliminates rows A and B because if Bernard had heard 5 or six, Bernard would immediately know the exact location of the ball (but Albert is 100% sure that Bernard is confused).
This elimination of A and B is new knowledge for Bernard. He confirms that he was confused, but now he isn't. This means it's not 1 because he recently discovered that it has to be C or D, but there are balls in both C1 and D1 which means he would still be confused if that were the case.
With all this knowledge, all that's left is a row with one ball, and a row with two balls. Albert says he is not confused anymore, so it has to be the row with one ball.