solution for Albert, Bernard and Cheryl birthday puzzle

The answer is July 16.

Explanation:
Albert knows the month and Bernard know the day (date).

1.Albert:        I don't know when Cheryl's birthday is, but I know that Bernard does not know too.

That means : that day cannot be 18 or 19 , they are unique (if it is 18 or 19 Bernard knows the birthday exactly, contradicting) .


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

Also Albert was sure that Bernard doesn't know the birthday , with only knowing the month. Hence the month cannot be May or June ( as those months have the dates 18 and 19).


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


2.Bernard:     At first I don't know Cheryl's birthday is, but I know now.

That means the day cannot be on 14, as  it will confuse Bernard (August 14 and June 14).


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


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

That means the month cannot be August, as it will confuse Albert (August 15 and August 17).


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

Now, I  also know when Cheryl's birthday is....

July 16 :D



Here is a paradox related to birthday you might be interested in.


BIRTHDAY PARADOX


9 comments:

  1. I still didn't get why you eliminate may 15 and 16

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    1. I hope you understood how we eliminated dates June 18 and May 19.
      Now Albert (who only knows the month) was sure that Bernard (who only knows the date (day) ) also didn't know the birthday. If the month that Albert had was either June or may then Albert cannot say for sure that "Bernard does not know too", since the date could be May 18 or June 19 in that case. Hence the month that Albert had cannot be May or June. Thus all the dates from those months are eliminated.

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    2. NO, this is where your logic is flawed. If I am told the month only, and that it is May, then it could be May 15th or May 16th. The other person could be told it is the 15th of a month, or 16th, and they would still have two choices for each. So you cannot illiminate May. You can, howeer, Illiminate June 17th, because everyone knows June 18th is not possible, and so knowing it was June would give me the exact answer, which is not permitted.

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    3. If Albert was told May he cannot be 100% certain that Bernard wasn't told 19 and therefore know the answer. Since Albert is 100% certain Bernard doesn't know the answer then Albert wasn't told May (and the same reasoning applies to why Albert wasn't June either)

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  2. "Also Albert was sure that Bernard doesn't know the birthday , with only knowing the month." -> How can this statement be true? How can Albert be 100% sure that Bernard does not know when it is Albert saying the 1st statement?

    The answer can either be June 17 or August 17

    Cheryl told Albert the month
    Cheryl told Bernard the day

    Albert's 1st statement is obvious. since there is no way he can know the birthday as all months are not unique. He "pretends" Bernard does not know also but there is no way he can be sure.

    Bernard said "at first I did not know" so this statement eliminates June 18 and May19 because they are unique.

    Bernard said "but now I know" so this statement points to June 17 as this is the only remaining date that has a unique month. Given the fact that Bernard claimed he already knows, confirms that the day is 17. however, there is no way for Bernard to know if it is June or August. So actually Bernard is only "pretending to know both the month and day" because he absolutely know the day is 17.

    Albert also noticed that June 17 is the only unique date. Since Bernard claimed to already know, then Albert now knows the day is 17. Albert's last statement is true, but only he (and Cheryl) knows the exact date

    ReplyDelete
    Replies
    1. since the month that Albert got was July (from my solution) he was sure that Bernard also doesn't know the birthday (the dates 14 and 16 from the month July could be confused with May 16 and August 14)

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  3. The official answer is based upon the assumption that Cheryl may have told Bernard either 18 or 19. If that is the case, then Albert can only be certain that Bernard does not know (first statement) if the month choices (May and June) do not include a unique date. Thus, May and June can be eliminated.

    The unofficial solution of August 17 is based on the assumption that Cheryl would not tell Bernard either 18 or 19. The reasoning is that why would Cheryl want to have Albert and Bernard guess her birthday and then just give the answer away to Bernard, which she would do because there is only one date with 19 (May 19) and one with 18 (June 18). Thus, Albert can be certain that Bernard does not know because there are four remaining numbers (14,15,16 and 17), each of which appear twice in different months.

    To me, the assumption that Cheryl may have told Bernard 18 or 19 is not plausible. Why set up the puzzle and just give Bernard the answer at the outset? That is why I think August 17 is the more reasonable answer.

    ReplyDelete
    Replies
    1. Maybe she likes Bernard more?

      You make too many assumptions. The only information Albert definitively has is the month. Since he is sure Bernard can't know based only on the day, not only can it not be the 18th or 19th, but it can't be all of May or June. If Albert had been told either of those months, Bernard could possibly have been told a unique date.

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  4. This is why correct use of English is so important, contrary to what the trendy teachers in the UK tell us. Without specific, precise English, complex problems such as this become clouded and hard to solve, because the sloppy English leads to vagueness in the definition of the problem !

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