Cheryl’s Birthday

Cheryl’s birthday is one 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 tells the month to Albert and the day to Bernard.

Albert: I don’t know the birthday, but I know Bernard doesn’t know either.
Bernard: I didn’t know at first, but now I do know.
Albert: Now I also know Cheryl’s birthday.

When is Cheryl’s birthday?

If Albert knows that Bernard doesn’t know when the birthday is, then the birthday can’t be on May 19 or June 18. Also, Albert must know that the birthday can’t be on these dates, so May and June are completely ruled out.

If Bernard can deduce when the birthday is after Albert’s comment, then the birthday can’t be on 14th. The remaining possibilities are July 16, August 15, and August 17.

Finally, if Albert figures out when the birthday is after Bernard’s comment, then the date must be July 16.

We do not know where this puzzle originated from. If you have any information, please let us know via email.

Responses

      1. So Basically because July only has 2 days of possibilities. I got that from the beginning it could only be Binary answer ruling out August not to mention no 16th in August (indifferent) June was already ruled out. May became a Binary choice by process of elimination. Albert could be sure the date wasn’t May 19th we established that 1st round. How Did Bernard know to rule out May as the month?

        1. The same way we figured it out… If the month was May, then Albert wouldn’t say in the beginning that he knows that Bernard doesn’t know the date.
          I know it sounds confusing:)

        2. It’s a given Bernard does not know the date How does Albert Know Bernard does not know for sure, What EXACTLY allows Bernard to rule out May?
          (other than saying he and Bernard dont know)
          We understand that both men realize it’s between 4 possible dates collectively and 2 each respectively. Allowing the statement Albert didn’t know neither did Bernard has no merit its a given. Accepting that fact destroys the logical thought process. Such as 18 or 19 ruled out that’s a solid fact (Bernard would have known)

        3. Bernard can rule out May because he hears Albert’s statement. Specifically, if the month was May, then Albert could not rule out May 19. If the date was May 19, Bernard would figure out the date immediately. Thus, since Albert says “Bernard does not know the date”, the month can’t be May.

          It is tricky, both to explain and to grasp, but this is all that’s needed to rule out May:)

        4. What exactly was it that ruled out May? Ruling out the 18th and 19th is evident only one of those so Bernard would know that’s a clear explanation. Ruling out June 17 is clear because that leaves only 1 choice for June and Albert wold figure that. What clear explanation ruled out May other than him saying he didn’t know. Saying he didn’t know in it self rules out nothing

        5. If Cheryl says “Bernard does not know the date”, we will be able to rule out only May 19 and June 18.
          However, if Albert says “Bernard does not know the date”, we will be able to further rule out the entire months of May and June.
          The key idea is that Albert knowing that Bernard does not know gives extra information, more than just Bernard not knowing.

          Assume Albert was told that the month is May. Then, Albert knows it is possible that the date is May 19, in which case it is possible that Bernard knows the date. However, Albert is sure that Bernard does not know the date and therefore, he can’t be told that the month is May.

  1. So the 2 are not aware that the other only has one half of the puzzle. The 2 are under the impression that the other may know both halves?

        1. Hi elliot. If the birthday was on May 19 or June 18, then, since these are the only 18/19 dates, Bernard would know when the birthday is.
          Now, if the birthday was in May or in June, then Albert couldn’t write off these possibilities, and therefore couldn’t be sure that Bernard does not know when the birthday is.

        2. Why isn’t it possible for the other dates?? Beside the first deduction

        3. The claim is that if the birthday was, say on May 15, then Albert would have been told only “May”, so for him, there would have been a possibility that the birthday is on May 19. Therefore, he could not be sure that Bernard did not know when the birthday is.

        4. Yeah, but if Albert was told “May” why would he include any other months? Likewise, If Bernard was told “19” he wouldn’t have any other dates.
          Wouldn’t it be more like:
          May 10 May 19
          May 13 September 19
          May 19 October 19
          May 20 December 19

        5. That’s the point, Sandwich. Since May 19 would ensure that Bernard does not have any other dates, Albert must be sure that the date is not May 19. If he was told “May” by Cheryl, then he can’t be sure about that and can’t make the statement “Bernard does not know when the birthday is.”