article_snippet.sent: but I know that Bernard does not know too.
article_snippet.sent: So, firstly, for Albert to be 'certain' that Bernard cannot know the answer - as suggested in the first statement Bernard makes - we can deduct that her birthday is not in May or June.
article_snippet.sent: If Albert had been given May or June as the month, there is no way Albert could be certain that Bernard doesn't know her birthday.
article_snippet.sent: Bernard, after all, might have been the number 18 or 19.
article_snippet.sent: For Albert to be 'certain' that Bernard doesn't know, Albert must have been given a month that does not contain one of these 'unique' dates - i.e. July or August.
article_snippet.sent: Albert's disclosure now gives Bernard the clue Bernard needs, and says Bernard now knows her birthday.
article_snippet.sent: This is because Bernard realises Albert has ruled out May and June because of the 'single number' aspect above.
article_snippet.sent: says Bernard knows which is her birthday.
article_snippet.sent: This means her birthday must be the only remaining date in the month Albert was originally told.