Spoiler Alert !! Singapore maths puzzle solution - when is Cheryl's birthday ?

How to solve the birthday riddle (supposedly) asked to Singapore schoolkids on a maths test that's been going viral (and driving people crazy) :

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"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 I don't know when Cheryl's birthday is, but I know now."
Albert: "Then I also know when Cheryl's birthday is."

So when is Cheryl's birthday ?"
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The question was posted on the Guardian website:

...and Kenneth Kong's FB page

[leovanhorrik]

Best answer I've found on youtube. At first I did not understand why one could rule out May and June. Now I do understand. If Albert was given May or June, he couldn't be sure saying that Bernard did not know too. Therefore it can't be May or June.

Many thanks for your explanation.

[aladinnotrebienaime]

very good and simple explenation for cheryl's birthday

[paulobouhid]

This problem is wrong from the very beginning. This kind of problems, envolving logically reazoning assume that A and B are "perfect logicians". And a "perfect logician" would never state the second part of A´s first statement ("B doesn´t know either"). A perfect logician would figured out that stating this, B would be able to solve the puzzle, as he actually did!!

[KiterTMK]

Bernard confirmed that at first he didn't know, which implies it has to be a double value. You cannot eliminate May because it contains numbers that occur twice in the table.

If Bernard would have known, Albert could tell that it isn't a double value, eliminating all the double 14, 15, 16 and 17, leaving only the 18th and 19th. Poor Albert still wouldn't know if it's May or June and there is no way of telling.

The opposite is true.

Knowing = eliminating all the doubles.
Not knowing = eliminating all the uniques.

[bugscom]

This makes no sense to me. Now I'm even more confused.

[TheSagitax]

If you assume that Albert said "I know that Bernard does not know too" because he waited for Bernard to say the date - but Bernard remained silent - than the answer is August 17th.

Otherwise if you assume that Albert said "I know that Bernard does not know too" without waiting for Bernard to say anything - than the answer is July 17th.

[WaqasAhmad-votg]

If Albert does not know the dates then how can he claim that Bernard does not know?

[brankomaksimovic]

Wrong, dont eliminate May and June, but numbers 18 and 19. Than you have open way to June 17. as an easy answer to this puzzle. She whispered to A "June" and to B "17". It really works, try it for yourself...