Solution to Singapore maths question that stumped the world

Singapore maths question stumped the world

The following question has stumped the world. It was circulated that this is a fifth grader exams question, but later verified that this is actually 14 year old questions

Problem

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?

Answer

The answer is 16 July!

How come? I'll explain later. But first imagine that Albert is holding a paper with Month July written on it, and Bernard is holding a paper with number 16 written on it.

The following is what happen inside their head, sometime come out from their mouth (written in bold)

Albert looking at the word July in his paper : "hmmm... Cheryl birthday is in July, but there are two possibilities 14 July or 16 July. I can't tell what day is in Bernard hand but it must be 14 or 16. Hmm.. if it is 14 than Bernard wouldn't know the month, because it could be 14 July or 14 August. If it is day 16 is in Bernard hand, he couldn't tell the month either for there are two possible answer 16 May or 16 July. Ha, Bernard couldn't tell Cheryl birthday either. Oke Cheryl, I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too."

Bernard looking at number 16 in  his paper : "Wait, indeed there are two possibilities with day 16, 16 May or 16 July. But, how can Albert know that I can't tell which month. He must have known that the day I have is not unique. Let me see, only day 19 (May) and 18 (june) that are unique, the rest are not unique. Albert can't have May or June then, otherwise he wouldn't be sure I didn't not know Cheryl birthday. Oh. it must 16 July, because there are no 16 August! oke Cheryl,  At first I don’t know when Cheryl’s birthday is, but I know now."

Albert surprised. "He didn't know before, but after I told him that I knew that he didn't know, now he knows. What happen? I see! He must have eliminated month May and June thinking that only in May and June that one with a specific day can tell exactly the month. So he knows it must be in July. He's clever, hmm... boleh juga. But what day is in his hand? 14 or 16? If it was 14, Bernard still have to decide between 14 July or 14 August, so it must be 16, because there is no 16 August! 16 of July it is! Then I also know when Cheryl’s birthday is."

The above 'conversation' happen inside Albert and Bernard head. How can I, as a third person know what is inside their head? I'll tell you a secret. I am a detective. But please don't tell others! As a detective I work like Sherlock Holmes, following clues that lead to conclusion. I read all Enid Blyton book The Famous Five, The Secret Seven and other great books of hers. These are the books that inspire me to think as if I am a detective.

Oke, here is my explanation. There are three clues:

Clue #1 : (Albert) I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.

By stating that Bernard can't tell Cheryl's birthday, Albert tells me that the day in Bernard hand cannot be unique day (day that only occur in one month only) Day 18 or 19 are unique, because if Bernard has number 18 or 19 he would know Cheryl's birthday right away. . How does Albert know? Remember that Albert know the month. By looking at the month he knows that the month in his hand does not contain unique day (18 or 19). This must be July or August.

From the clue #1 we can tell that Cheryl's Birthday must be in July or August. i.e: July 14, July 16, August 14, August 15, August 17

Clue #2 : (Bernard) At first I don’t know when Cheryl’s birthday is, but I know now.

From this statement, we know that at first there are many possiblities but Albert statement eliminate other possibilities giving only one possible date for Bernard. From 5 remaining possibilities explained above only day 14 that has two possibilities, i.e 14 July and 14 August. Definitely, it is not 14 that is in Bernard hand, otherwise he can't be sure.

From this clue, we eliminate two impossible date, and remain 3 possible date July 16, August 15, August 17

Clue #3 : (albert) Then I also know when Cheryl’s birthday is

What month is in Albert hand? From remaing possible date, it could be July or August. If it was August, Albert wouldn't know exact date because there are still 2 possible date. So it must July! Therefore Cheryl's birthday is July 16!

See?