july 16 is her birthday.
explanation;
there are only two dates with unique numbers; may 19 or june 18. therefore if bernard was given a date of either 18 or 19, he’d know right away. albert then says bernard doesn’t know which means the month he was given wasn’t may and/or june. bernard has this much figured out so far, and if he had been told 14 he wouldn’t know the answer as there are still two forteens left (july and august) leaving july 16, august 15, & august 17. bernard must have been given the number 16, because when albert says he knows too, that would rule out August, which still has two remaining dates.
