When is Cheryl’s Birthday?

So when is Cheryl’s birthday? That’s a question confounding thousands of people around the world Monday as a test question from Singapore goes viral.

Puzzle: 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 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?

Solution:
The solution involves using logic to deduce the dates which can’t possibly be Cheryl’s birthday.

The dates range from 14 to 19 among the 10 that are given with only 18 and 19 occurring once.
Albert, having seemingly been told the month rather than the day, first says he doesn’t know when her birthday is – eliminating both 18 and 19 as possible days.
If Cheryl had told Albert that the month was May or June, then the day could have been May 19 or June 18, and Bernard may have known the right day. But, as the question says, Albert knows Bernard does not, meaning that Cheryl has said her birthday is in either July or August.

Out of the five remaining days in July and August, the day ranges from 14 to 17, with 14 appearing twice.

If Cheryl told Bernard her birthday was on the 14th, then he would not have known but, he does, meaning it can’t be on the 14th.

That leaves only 3 possible days: July 16, August 15, and August 17.

After Bernard speaks, saying he knows the birthday given that information, it eliminates August from being a contender since he still wouldn’t have known
whether it was August 15 or 17.

Therefore, Cheryl’s birthday is on July 16.

20 Thoughts on “When is Cheryl’s Birthday?

  1. Sumit Sharma on April 16, 2015 at 4:20 am said:

    There are only two dates with unique numbers: May 19 or June 18. If Bernard was given a date of either 18 or 19, he’d know right away. The fact that Albert says Bernard doesn’t know means the month he was given wasn’t May or June. Bernard has now figured this much out, and if he had been told 14 he wouldn’t know the answer as there are still two 14s left (July and August) leaving July 16, August 15 and August 17. Bernard must’ve been given the number 16, because for Albert to say he knows too would rule out August, which still has two remaining dates. That leaves the answer: July 16.

  2. chatur ramalingam on May 15, 2015 at 8:37 pm said:

    dear sumit sharma,
    i think your solution so farji…..
    dont play with emotions….
    plz reply with the correct solution

  3. Guest on July 28, 2015 at 6:29 am said:

    Not a satisfied answer, its all assumption then we can assume her birthday falls on may 15 also…..or any other date… please give a correct explanation.

  4. Pranay H. on August 10, 2015 at 3:15 pm said:

    I didnt get the explaination. SO PLZ EXPLAIN ME PROPERLY ………..

    • Ketan Kankapure on October 16, 2015 at 2:58 pm said:

      Dates Given :
      ——————————–

      May | |15|16| | |19|
      June | | | |17|18| |
      July |14| |16| | | |
      August |14|15| |17| | |

      ——————————–
      Say Albert=A ; Bernard=B ;Cheryl=C
      ———————————————————————————————-

      A says: B doesn’t know the date

      This means:B has more than one options,that’s why he doesn’t know
      Ex.Say B has 17 , A says he can’t deduce the month as 17 appears in Juna as well as in August

      So,If the date were 18 or 19 then there would not have been any confusion for B,as
      these dates doesn’t repeat in given data and B would have known the month to be May/June.
      Therefore 18,19 are ruled out.

      A says:He doesn’t know too

      It means the month is not June(18th date)/May(19th date)
      Because if the months were June/May then A could have told that B doesn’t know.
      That’s why these months are also ruled out.
      ———————————————————————————————–
      Now the data becomes :

      July |14| |16| | | |
      August |14|15| |17| | |

      B says: Now he knows

      It means , for B to know the birthdate, the dates he knows,doesn’t fall in more than one month
      That’s why he says confidently that he has no confusion now

      So both occurences of 14 are ruled out as they fall in July as well as August.

      ————————————————————————————————
      Now the the data becomes

      July | | |16| | | |
      August | |15| |17| | |

      NOW B says :Now I know

      :-) It means there is no confucion for A now, which means the month which A knows has only one date left.
      That’s why he has no confusion anymore.

      Here Only July has one date left i.e. 16th

      Therefore the month is “July” AND date is “16″

      —————————————————————————————————–

  5. good question,
    i think this has something to think
    the problem is here; when albert can say her birthday we can skip aug 15,17 but if the birthday was in august how albert able to tell the birthday?? anyway practicality is not matter it helped me to spent sometime

    • Ketan Kankapure on October 16, 2015 at 2:58 pm said:

      Dates Given :
      ——————————–

      May | |15|16| | |19|
      June | | | |17|18| |
      July |14| |16| | | |
      August |14|15| |17| | |

      ——————————–
      Say Albert=A ; Bernard=B ;Cheryl=C
      ———————————————————————————————-

      A says: B doesn’t know the date

      This means:B has more than one options,that’s why he doesn’t know
      Ex.Say B has 17 , A says he can’t deduce the month as 17 appears in Juna as well as in August

      So,If the date were 18 or 19 then there would not have been any confusion for B,as
      these dates doesn’t repeat in given data and B would have known the month to be May/June.
      Therefore 18,19 are ruled out.

      A says:He doesn’t know too

      It means the month is not June(18th date)/May(19th date)
      Because if the months were June/May then A could have told that B doesn’t know.
      That’s why these months are also ruled out.
      ———————————————————————————————–
      Now the data becomes :

      July |14| |16| | | |
      August |14|15| |17| | |

      B says: Now he knows

      It means , for B to know the birthdate, the dates he knows,doesn’t fall in more than one month
      That’s why he says confidently that he has no confusion now

      So both occurences of 14 are ruled out as they fall in July as well as August.

      ————————————————————————————————
      Now the the data becomes

      July | | |16| | | |
      August | |15| |17| | |

      NOW B says :Now I know

      :-) It means there is no confucion for A now, which means the month which A knows has only one date left.
      That’s why he has no confusion anymore.

      Here Only July has one date left i.e. 16th

      Therefore the month is “July” AND date is “16″

      —————————————————————————————————–

  6. Can the admin plz explain the solution again?

  7. Ketan Kankapure on October 16, 2015 at 2:54 pm said:

    Dates Given :
    ——————————–

    May | |15|16| | |19|
    June | | | |17|18| |
    July |14| |16| | | |
    August |14|15| |17| | |

    ——————————–
    Say Albert=A ; Bernard=B ;Cheryl=C
    ———————————————————————————————-

    A says: B doesn’t know the date

    This means:B has more than one options,that’s why he doesn’t know
    Ex.Say B has 17 , A says he can’t deduce the month as 17 appears in Juna as well as in August

    So,If the date were 18 or 19 then there would not have been any confusion for B,as
    these dates doesn’t repeat in given data and B would have known the month to be May/June.
    Therefore 18,19 are ruled out.

    A says:He doesn’t know too

    It means the month is not June(18th date)/May(19th date)
    Because if the months were June/May then A could have told that B doesn’t know.
    That’s why these months are also ruled out.
    ———————————————————————————————–
    Now the data becomes :

    July |14| |16| | | |
    August |14|15| |17| | |

    B says: Now he knows

    It means , for B to know the birthdate, the dates he knows,doesn’t fall in more than one month
    That’s why he says confidently that he has no confusion now

    So both occurences of 14 are ruled out as they fall in July as well as August.

    ————————————————————————————————
    Now the the data becomes

    July | | |16| | | |
    August | |15| |17| | |

    NOW B says :Now I know

    :-) It means there is no confucion for A now, which means the month which A knows has only one date left.
    That’s why he has no confusion anymore.

    Here Only July has one date left i.e. 16th

    Therefore the month is “July” AND date is “16″

    —————————————————————————————————–

    • Couldn’t understand how the months May and June were ruled out.

    • IBRAHIM KHAN on January 26, 2016 at 9:34 pm said:

      If B doesn’t know, that means the day told to him is other than 18 or 19.
      So the day can be 14 or 15 or 16 or 17.

      So based on the above statements, how r u people eliminating May and June ????

      • Praveen on March 8, 2016 at 2:59 pm said:

        It’s so Ibrahim because it’s not about that B doesn’t know; it’s about A is sure that B doesn’t know;A can be 100% sure only in case when the month which has been told to him is having all the dates which occur twice

  8. For the people who had trouble understanding the solution:

    Statement1 – Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.

    Now, Consider Cheryl gave Albert the month as either May or June. In such a case, Albert couldn’t say for sure that Bernard doesn’t know the birthday. Because, the dates could have been 18 and 19 which Albert doesn’t know. Hence May and June are ruled out.

    Statement2 – Bernard: At first I don’t know when Cheryl’s birthday is, but I know now.

    After hearing statement 1, Bernard knows (as we all know now :)) that its not May/June. Now, had it been the 14th, he wouldn’t have known the birthday for sure as both July and Aug have that date. So Albert now knows it could be either of 15th, 16th or 17th.

    Statement3- Albert: Then I also know when Cheryl’s birthday is.

    Had it been August, Albert couldn’t have known for sure since it can be 15th or 17th Aug. Hence it is July. And the Birthday is on July 16.

  9. I agree, you can’t rule out May and June just because Bernard doesn’t know the day.

    Here’s my answer:

    If the day were 18 or 19, Bernard would know the birthdate. So we know it’s not May 19 or June 18.

    Since Albert knows that, and he still doesn’t know the birthday, we now know that it can’t be June 17 (the other remaining day in June).

    Since Bernard knows that it can’t be June 17 either, he now knows that it’s the other 17. So, 17 is the day, and August 17 is the birthday.

  10. @ABC
    If Aug 17 were the birthday, Albert will know its August and Bernard will know its 17th.

    In such a case how can Albert say that Bernard does not know the Birthday? (as per the first statement)

    • Praveen on March 8, 2016 at 2:56 pm said:

      Albert can say in this case because he knows that all the dates of August ie 14,15 and 17 occurs twice in possible dates list so just by knowing the date Bernard cannot come to know the month exactly.

  11. Reasons for ruling out May and June.
    Albert know for sure that Bernard does not know Cheryl’s bday . So, if Cheryl’s bday could have been in May or June, there is a possibility that it cud be May 19 or June 18. Thus There was a chance for Bernard to know the exact bday, it he was given the date as 18 or 19. For Albert to become 100% sure that it’s not may 19 or June 18, we must reject May and June as months altogether.
    For instance: Albert knows That bday is in May, so it could be 15,16 or 19 May. But he does not know what Bernard knows. So to be100% sure that Bernard does not know the date, we must rule out May and same applies for June.

  12. Think you are bernard, you didn,’t get 18 or 19, or else you would have given th answer, and then albert says that you wouldn’t know the answer hinting that the remaining answer id not in the unique digits remaining of may and june, and this is how may and june are eliminated. The hint is albert need not have said i did’nt know the answer.

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