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 didn’t know when Cheryl’s birthday is, but I know now. Albert: Then I also know when Cheryl’s birthday is. When is Cheryl’s birthday?

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It's that Singaporean puzzle again

Answers

2016-02-23T09:30:01+05:30
I'll try to keep it simple.

Albert knows the month, while Bernard knows the day. If Bernard had got the number 18 or 19, then he can easily guess that the month is June or May respectively. But, Albert is certain that Bernard doesn't know. Meaning the birthday is not in June or May.

So somewhere in July or August. After Bernard realizes that Albert doesn't know the date either, he finds out Cheryl's birthday. Meaning that the day he was given is not 14 (if it had been then it could have been in either remaining months).

Through this the dates we are left with are July 16, August 15 and August 17. Note how there is only one for June and two for August.

After Bernard's affirmation that he knows Cheryl's birthday, Albert realizes her birth date too. This means that he must have been told the month July; if he was told August then he would have two dates to think about which would make him unsure.

That leaves us with only one date, which is July 16.
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