The answer is indeed July 16, but I found most of the explanations given so far so confusing that many people end up being more confused. Here I will attempt to explain to you why the answer is July 16. Let’s replace Albert with A, Bernard with B, and Cheryl with C. Now the question becomes as follows:
———————————————————————————————————
A and B just become friends with C, and they want to know when her birthday is. C gives them a list of 10 possible dates.
May 15 , May 16, May 19
June 17, June 18
July 14, July 16
Aug 14, Aug 15, Aug 17
C then tells A and B separately the month and the day of her birthday respectively.
A: “I don’t know when C’s birthday is, but I know that B does not know too.”
B:”At first I don’t know when C’s birthday is, but I know now.”
A:”Then I also know when C’s birthday is.”
So when is C’s birthday?
———————————————————————————————————–
The best way to understand why the answer is July 16 is to, at all times while analysing this question,
(1) remember that A knows that the MONTH of C’s birthday is July and B knows that the DAY of C’s birthday is 16.
(2) remember to think the way A and B would think, not the way YOU would think.
The significance of A’s statement “I know that B does not know too.”
Why is A so sure that B doesn’t know? Because, A knows the month is July, and July can be either July 14 or July 16. This means A knows that B has been told the number 14 or 16, and since both numbers appear twice, B wouldn’t be able to pinpoint the exact birthdate.
However, by letting out that B doesn’t know for sure, A has actually given B a strong clue. What is that clue? The clue (for B) is, the month cannot be May or June. Why? B is now thinking: IF the month has been revealed to A as May, then A wouldn’t be so sure that I (B) don’t know, because I could have been told the number 19 and I would know! (because there is only one 19). Similarly, B would be thinking: IF the month has been revealed to A as June, then A wouldn’t be so sure that I (B) don’t know, because I could have been told the number 18 and I would know! (because there is only one 18). Thus B would say to himself: It cannot be may or june (else A wouldn’t be so sure that I don’t know). So I will look at July and August. I (B) know it is 16, and there is only one 16 left! So it must be July 16.
This caused B to say “I know now”. : )
The significance of B’s statement “I know now.”
A suddenly realises that B suddenly knows the answer after A’s first statement. A is now thinking: how did B know? A realised that B has discovered that the month is either July or August. A is now thinking: since B CAN pinpoint exactly, then the number that B knows cannot be 14, since both July 14 and August 14 exist. So July 14 is out! But I (A) KNOW that it IS July, so it must be July 16! (the only July date left).
That is why A finally said, “THEN, I also know when C’s birthday is.”
In conclusion, it can be seen that B could find out only AFTER A had said that B didn’t know, and A could only determine C’s birthday AFTER B had said that B was able to pinpoint the answer after A’s first revelation.
Ok, now please take Panadol or go to sleep or both.
Rgds,
Ilyasa
———————————————————————————————————–
If you want to practise your logic deduction skills further, you may try some easier permutations of the above question as listed below.
Question 2:
B:”I don’t know when C’s birthday is.”
A:”Then I know.”
B:”Then I know too.”
So when is C’s birthday?
(Answer is at far bottom of page)
Question 3:
B:”I don’t know when C’s birthday is.”
A:”Neither do I.”
B:”At first I don’t know, but now I know.”
A:”Oh thanks. Now I know too.”
So when is C’s birthday?
(Answer is at far bottom of page)
ANSWERS: Q2: June 17; Q3: August 17.