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#14




A1: Albert was told July or August
B1: Bernard was told 14 Now Albert says, I know, only because you don't. If Albert was told July, he would already know that Bernard wouldn't know the birthday, because he would know that 14 and 16 are the only options that Bernard had, and that wouldn't be enough to narrow it down. Since Albert is getting more information from this statement, that means it has to be August. 
#15




Because Albert would not have been hahaha appreciative that Bernard still didn’t know for sure when it was. Because if he was told July, he would have just known it was July 16th in the classic example where Bernard at first didn’t know it and then now knows it,
But here he’s revealing he would have no way of knowing it if it wasn’t for the case of the 14th, which means it has to be the month where you can’t know what other date it is if it isn’t the 14th 
#16




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After the first statement, if Bernard had been told 15,16 or 17 then he'd now know. He doesn't, so it must be 14. Albert now knows, as he knows the month. But that would be the case if it was July or August.
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#18




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#20




'Today is my one hundred and
eleventh birthday: I am eleventy one today!' 'Hurray! Hurray! Many Happy Returns!’ they shouted, and they hammered joyously on the tables. Bilbo was doing splendidly. This was the sort of stuff they liked: short and obvious. 
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