Thanks for the explanation, but I cannot follow on this line

Since he knows that Bernard doesn’t know given just the row, each ball in that row is in a column that contains more than one ball.

Why is that? Why couldn’t it be A2 or A3? In this case neither Albert nor Bertrand could tell what row/column this was either, because it would be in a row/column with another ball. How can you exclude any row with overlap with any single-ball columns?

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Same!