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The Cheryl's Birthday problem

Here's to obsessions. And math problems. And visual aids to thinking. And to Singapore where teaching kids how to think takes precedence over doofus regurge.

Here's the problem:

Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.
May 15 16 19

June 17 18

July 14 16

August 14 15 17

Cheryl then tells Albert and Bernard separately the month and the day of her birthday, respectively.

Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know, too.

Bernard: At first, before Albert spoke just now, I did not know when Cheryl’s birthday is. But with that added information now I do know her birthday.

Albert: Then now I also know when Cheryl’s birthday is.

When is Cheryl’s birthday?

That's a Sec 3 Singapore high school whiz-bang Olympics test question.
Hint: draw a matrix diagram. Work it through using the intensionalities/check-offs to eliminate options.

Explanation below the fold. .

Enjoy !!

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