Interesting Singapore P5 math puzzle

[Peter]

This is a problem from Singapore P5 Math Olympiad competition that ccreates a stir on the Internet. It is about year 6 level here. However people argue over 2 possible solutions depending how people understand the English. Also it depends on what assumptions you start with about who knows what.

[2016ss04]

Hi Peter,

Is the answer May 19th?
I choose the answer because Bernard knew when her birthday was from one piece of information, the day. Therefore, the number must only appear in the list once.

Please tell me if my answer is correct.

Thanks in advance.

regards
2016 ss04