[polak]

Originally Posted by annasuave

rd-aaron has it. I disagree with Polak's solution.

Spoiler!

Cheryl tells Albert the month she was born. She tells Bernard the day.
Neither Albert or Bernard can figure it out from the info she gave.
When Bernard hears Albert say that "I don't know, and I know Albert doesn't either", then Bernard knows the answer.

From this statement we know that it cannot be June 18 or May 19. (Because, Albert, knowing the day would have figured that out on the spot as both 18 and 19 are unique in the puzzle.)

At this point, Bernard (knowing the month) knows its NOT May or June.

That leaves July and August - both of which have days in common, except for the 16th.

Bernard can then figure out that the only non-repeated day is the 16th, so her birthday must be July 16.

I think the question is poorly worded, grammatically speaking. Kind of a mean thing to do to kids in a high-pressure test situation. Its not really clear that Bernard and Albert are able to hear each other. But then again, maybe that's a cultural assumption in Singapore?

You've done what I did a million times and flipped what Albert and Bernard know.