# That ‘P5’ becomes S3 Math Olympiad Question – When is Cheryl’s birthday? – An in-depth discussion

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:

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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?

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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

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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.

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