Can you solve this mind-boggling problem?

[Materia-Blade]

Hynad said:

It can't be May 19 or June 18. Because Bernard would know the birthday right away.
Albert doesn't know when it is with just the month, but because of that Bernard now knows when it is.

Now because Bernard could figure out based on Albert's claim, Albert now know when the birthday is as well.

Since Albert can't know what day it is in August, and Bernard can't know which 17 it is, and since Albert couldn't have been certain that Bernard doesn't know if it is in June, because 18 doesn't repeat anywhere else other than June (leaving only one other possible day in that month), it can be no other day than August 17.

except that the same can be said about 14 and 15.