Can you solve this mind-boggling problem?

[theprof00]

Materia-Blade said:

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.

and 14 and 16, and 15 and 16

if those months and dates are given to albert and bernard respectively, bernard wouldn't ever be able to figure it out. However, because we know Bernard knows, we can then rule them out.

So, it has to be the 17th.

imagine this:

Albert is given may and bernard is given 15.
The first statement works, however, given the knowledge that bernard cannot know (from albert) bernard can't actually make a proper conclusion as to what the month is, since two months share the number.
The same would apply if we assume may and 16 are given as well as the other combinations of july, august, 14, and 16.

Bernard can NEVER figure it out. Therefore, none of those can be right.