Cheryl’s Birthday


differences between to know something or to deduce something




Albert and Bernard just become friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates:

May 15       May 16      May 19

June 17      June 18

July 14       July 16

August 14       August 15      August 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?

The solution:

Albert knows (not deduces) that Bernard does not know, too. 18 and 19 are once, and indicate the specific dates, which means that Bernard must receive a different number (day).
[we eliminate:
May 19 and June 18]

When Albert learns that Bernard does not know too and Albert still does not know the date it means that the month is not June. Because if it was June Albert would know the date but he do not know the date.
[we eliminate:
June 17]

This information is determining for Bernard only in one case - if the number is 17 and this means that the day was 17.

Therefore, the date is August 17.

 Cheryl’s birthday is on August 17.

to know something or to deduce (to know of deduction)? What does mean to know? It is a question!

The Official solution

Out of the 10 dates, the day ranges from 14 to 19, with only 18 and 19 occurring once. If the day is Cheryl's birthday is 18 or 19, then Bernard would have known when Cheryl's birthday is since Cheryl has told him the day of her birthday.

But why does Albert know that Bernard does not know?

If Cheryl has told Albert that her birth month is May or June, then it is possible that her birthday may be May 19 or June 18. This means that Bernard may know when Cheryl's birthday is. The fact that Albert knows that Bernard does not know means that Cheryl has told Albert that her birth month is either July or August.

Initially, Bernard does not know when Cheryl's birthday is, but how did he know after Albert has first spoken?

Out of the 5 remaining dates in July and August, the day ranges from 15 to 17, with only 14 occurring twice.

If Cheryl has told Bernard the day of her birthday is 14, then Bernard would not have known. The fact that Bernard knows means the day of her birthday is not 14. So now we are left with 3 possible dates: July 16, August 15 and August 17.

After Bernard has spoken, Albert now knows when Cheryl's birthday is. If Cheryl has told Albert her birth month is August, then Albert would not have known because there are two possible dates in August.

Cheryl's birthday is on July 16.



The organizer of the competition explains why their version is correct, that is Albert first opened his mouth. Only that it is not so obvious, because in the first Albert's sentence is: "I know that Bernard does not know too" and one can be consider that Albert does not know the date and know that Bernard did not know, too. Conclusion: They told each other that they did not know.

The creators of the competition should pay attention to another aspect, for their version supported by the fact that otherwise the last sentence would not have added value (although they are tricky puzzles, but just in this case catchiness rather would not be seen).

In the case of the solution with August 17 the statement:

Albert: "Then I also know when Cheryl's birthday is."

could not be at all.

However, in the case of the official solution, if the brain teaser had not the last sentence only Bernard could know an answer and we could only agree with the fact that there is a possibility that Bernard would know, but we would not know Cheryl’s birthday.





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