19th May. .. 19 only appears once
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Nope, 18 also appears only once and that is the key to solving the first part. If Albert knew there was the possibility that the day was 18 or 19 (if he'd been told May or June) then he wouldn't be able to say that he knows Bernard doesn't know either.
So... it's July or August?
And, it's probably not the 14th, because that's in both months.
Is her birthday on July 16th?
Thats what I get.
If albert knows Bernard doesnt know then that rules out any month with a unique day which rules out may and june. Otherwise he'd have to say bernard might know.
Bernard realises that and then says he knows which date is correct which he wouldnt know which month if it was the 14th so that rules out the 14ths
If cheryl had told albert it was august then he wouldnt know which of the remaining dates was correct so he must've been told july for him to know by the end.
Thats my reasoning anyway.
To use my phone in the car I deleted all my German contacts, it's now Hans free.