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An Early Friday Puzzler -- Birthdays

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An Early Friday Puzzler -- Birthdays

#1

An Early Friday Puzzler -- Birthdays

Alex Y

We've ween one like this here before, but this seems to be making the rounds again. I'll quote from the NYT column where I saw it:

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?

Re: An Early Friday Puzzler -- Birthdays

#2

And women wonder why

Henry Higginbotham

we can't remember their birthdays.

Re: An Early Friday Puzzler -- Birthdays

#3

Re: An Early Friday Puzzler -- Birthdays

Henry Higginbotham

I'm not very good at this sort of puzzle, but I'll take a stab at what looks like the easy part.

I think it couldn't be May 19 or June 18 because there are no other 18s or 19s, and thus Bernard would have known immediately. That leaves only the 17th in July, which would make it too easy for Albert, and takes the 17th out of play for August.

Beyond that (if any of the above is even valid), I got nuttin'. It's getting awfully tempting to look for it on the Internet, but I'm being good for now.

Re: An Early Friday Puzzler -- Birthdays

#4

Re: An Early Friday Puzzler -- Birthdays

Larry Barrett

My friend offers this explanation for July 16:

1. Albert say he knows Bernard doesn't know. This means that the month must be July or August since if it were May or June, Bernard might know the answer if he were given the 18th or 19th.

2. Given that Bernard hears Albert's response, he now know the month must be July or August. If he were given the 14th he still wouldn't know which month, so he must have been given the 15th, 16th or 17th.

3. Albert now says he know too. So he is able to rule out the 14th also. My only guess as to how he knows is that Cheryl said they could figure out the date. Since August is ambiguous at this point because it has both the 15th and 17th, my guess is that the date must be July 16.

Re: An Early Friday Puzzler -- Birthdays

#5

Re: An Early Friday Puzzler -- Birthdays

Alex Y

I'm not very good at this sort of puzzle, but I'll take a stab at what looks like the easy part.
Don't sell yourself short; you are on the right track.

I think it couldn't be May 19 or June 18 because there are no other 18s or 19s, and thus Bernard would have known immediately
Exactly. And that context for Albert's response tells us something about what he knows of the month. One step at a time. See Larry's post.

Re: An Early Friday Puzzler -- Birthdays

#6

Right on the first two steps

Alex Y

And very close on the third. Step two gets it down to the possible dates. What must Albert know about the month that lets him be able to now claim to know her birthday?

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