1. Albert has July, so he knows all the days Bernard could have been given have duplicates. Thus, he knows Bernard doesn't know the birthday yet. 2. Bernard he

1. Albert has July, so he knows all the days Bernard could have been given have duplicates. Thus, he knows Bernard doesn't know the birthday yet. 2. Bernard hears this and knows Albert is holding on to either July or August. He holds a number that is unique within these 2 months. That is why he now knows the birthday. 3. Albert now knows that Bernard knows, and thus has a day that is unique between July and August. Which means it cannot be 14. 4. So among July 16, August 15, and August 17, the only way Albert can know for sure is if he is holding on to July. Therefore July 16.