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.
What I don’t understand is how Albert got the information from Bernard.
Written as it is, we can deduce the C3.
But how did Albert understand from Bernards sentence that it’s in the 3rd column?
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.