Apr 15, 2015

When’s your birthday? ~ A Singapore Math Problem With The Solution

Question:

Albert and Bernard just met Cheryl. “When’s your birthday?” Albert asked Cheryl.
Cheryl thought a second and said, “I’m not going to tell you, but I’ll give you some clues.” She wrote down a list of 10 dates:
May 15 — May 16 — May 19
June 17 — June 18
July 14 — July 16
August 14 — August 15 — August 17
“My birthday is one of these,” she said.
Then Cheryl whispered in Albert’s ear the month — and only the month — of her birthday. To Bernard, she whispered the day, and only the day. 
“Can you figure it out now?” she asked Albert.
Albert: I don’t know when your birthday is, but I know Bernard doesn’t know, either.
Bernard: I didn’t know originally, but now I do.
Albert: Well, now I know, too!
When is Cheryl’s birthday?

 Solution:

First Clue:
I don’t know when your birthday is, but I know Bernard doesn’t know, either.
How does Albert know that Bernard does not know?  Albert has no clue that Day is not 18th or 19th.  This means the month cannot be May or June.

Second Clue:
I didn’t know originally, but now I do.
After knowing Albert’s statement, Bernard now also knows that Cheryl’s birthday is not in May or June.  With this information, Bernard now knows the exact birthday.

This means it won't be 14th because there would still be two possibilities: July 14 and Aug. 14.

Last Clue:
Well, now I know too!
With 3 choices left (July 16th, August 15th, August 17th), Albert knows the birthday as well.  It is the same logical process again.  If Cheryl had told him August, Albert would not know the birthday.  It must be July then.

The answer is July 16.

 Fun?

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