Cheryl's Birthday

Well, Cheryl has taken the internet by storm.

If you are wondering "Cheryl Who?", it is the fine young lady who featured in an examination paper in Singapore, with her buddies Albert and Bernard.

The problem, for third grade students, went as below.

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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?
~~

Hope your head isn't spinning already. Spare a thought for the third grade kids. I am sure some of them would have come home crying after seeing this question.

The internet is ablaze with answers.

If you are keen to solve the problem, please pull out your pen, paper and pencils, and set your brains in motion.

If not, just scroll below.
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Some of them say July 16, while other say August 17.

Yours Truly begs to differ.

My choice is :- Cheryl's birthday is June 17.

Why do I say so?

Step 1
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.

With these statements, 
1. Albert made an assumption.
2. Bernard confirmed the assumption.

The assumption :- Bernard did not know Cheryl's birthday at the beginning.

The only way Bernard would not know Cheryl's birthday at the beginning would be when he gets a date other than 18 and 19.

If Bernard got 18th, he would know its 18 June.

If Bernard got 19th, he would know its 19 May.

This rules out 18 June and 19 May.

With this step, the data looks as below.

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

Step 2
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.

With these statements, once again, 
1. Bernard made an assumption (read - I know now)
2. Albert confirmed the assumption (read - Then I also know)

The only way for Bernard to know a date (and make an assumption) and Albert to know a month (and confirm the assumption), and thus, uniquely arrive at the correct birthday, is for the birthday to be 17 June.

Hypothesis (refer to the data at step 1 - pasted below for reference)
May 15      May 16      May 19
June 17     June 18
July 14      July 16
August 14  August 15  August 17

1. If the month was May, the date was ambiguous.

2. Similarly, if the month was July, the date was ambiguous 

3. Similarly, if the month was Aug, the date was ambiguous 

4. But if the date is Jun, the date is non ambiguous. That's the only condition under which Albert can confirm to Bernard's assumption.

Conclusion
This leads me to the conclusion that Cheryl's birthday is on 17 June.

Am I right or wrong? Views are welcome.

Hit the like button or share if friends if you like the reasoning and you agree with the answer.

If you think my reasoning is wrong, feel free to write a comment.

P.S. This puzzle came to my notice just a day after I told my friend, "Life is not about puzzles!!". This was God's own sweet way of telling me, "Son, yes, life is all about puzzles." :-)

Cheryl's Birthday Cheryl's Birthday Reviewed by Vyankatesh on Thursday, April 16, 2015 Rating: 5

1 comment:

  1. You're wrong.
    If Albert had been told June he'd know the answer (having eliminated 18), and so wouldn't say "I don't know he answer"

    ReplyDelete

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