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darkshadow23 said:
Albert knows the month but not the day. But he knows that Bernard is not able to know. So that cancels out the months of May and June. Why? Because of June 18 and May 19. 18 and 19 are not found anywhere else, so if Bernard knows the day is 18 or 19 then he knows her birthday.

So we have left. July 14, July 16, August 14, August 15, and August 17.

Bernard now understands the above and this let him figure out what her birthday was. The only way that he can know the date is if there is only 1 number. So that means we can cancel out July 14 and August 14.

Now we have: July 16, August 15, and August 17.

Then Albert says that he now knows her birthdate, and since Albert only knows the month then her birthdate must be July 16.

It should be said that it is because albert knows the month, that we can deduce it is the 16th. Albert can only know if his possibility had been reduced to one. And that only happens with july