Okay I'm taking a break for a moment to analyze a brain teaser. This one was posted to the New York Times:
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?
Several Solutions have been posted here and here. Unfortunately each has a flaw in its logic and is wrong.
The analysis begins soundly enough. Albert doesn't know, and he knows that Bernard doesn't know either. Since Bernard was only told the day we can rule out 19 and 18 since they each have only one month associated with them. That leaves us with the following possibilities.
May 15, 16
June 17
July 14, 16
August 14, 15, 17
Now we need to look back at the very first statement, Albert doesn't know. Albert only knows the month, so we can eliminate June, since it only has one day associated with it that's not ruled out. For some reason, both the Times and The Guardian eliminate May at the same time, but May is still a definite possibility. Bernard could have been told either 15 or 16, and the statement would still be logically true.
*Update* On reading the comments section, NYT claims that May has to be eliminated because otherwise Albert would not be able to make the statement that Bernard does not know either. i.e. If he had been told May he wouldn't be able to eliminate May 19th and definitively state that Bernard does not know either. However a person can infer from Cheryl's behavior and statements that she did not give such an easy answer to Bernard and not Albert.
That leaves us with the following possibilities:
May 15, 16
July 14, 16
August 14, 15, 17
The next statement is that Bernard did not originally know, but now he does. Remember he only knows the day. The only possibility at this point that satisfies this statement is August 17th. Bernard was clearly told 17, but could not deduce between June and August until June 17th was eliminated. The correct answer is August 17th.
The third statement is that Albert knows too. Once Bernard deduced the correct answer and revealed that he knew, Albert can use his powers of deduction to realize that August 17th is the only possible explanation.
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?
Several Solutions have been posted here and here. Unfortunately each has a flaw in its logic and is wrong.
The analysis begins soundly enough. Albert doesn't know, and he knows that Bernard doesn't know either. Since Bernard was only told the day we can rule out 19 and 18 since they each have only one month associated with them. That leaves us with the following possibilities.
May 15, 16
June 17
July 14, 16
August 14, 15, 17
Now we need to look back at the very first statement, Albert doesn't know. Albert only knows the month, so we can eliminate June, since it only has one day associated with it that's not ruled out. For some reason, both the Times and The Guardian eliminate May at the same time, but May is still a definite possibility. Bernard could have been told either 15 or 16, and the statement would still be logically true.
*Update* On reading the comments section, NYT claims that May has to be eliminated because otherwise Albert would not be able to make the statement that Bernard does not know either. i.e. If he had been told May he wouldn't be able to eliminate May 19th and definitively state that Bernard does not know either. However a person can infer from Cheryl's behavior and statements that she did not give such an easy answer to Bernard and not Albert.
That leaves us with the following possibilities:
May 15, 16
July 14, 16
August 14, 15, 17
The next statement is that Bernard did not originally know, but now he does. Remember he only knows the day. The only possibility at this point that satisfies this statement is August 17th. Bernard was clearly told 17, but could not deduce between June and August until June 17th was eliminated. The correct answer is August 17th.
The third statement is that Albert knows too. Once Bernard deduced the correct answer and revealed that he knew, Albert can use his powers of deduction to realize that August 17th is the only possible explanation.
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