Math Olympiad Question -Brthday Girl

[Deleted member 4993]

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?

 

[Ishuda]

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?

Interesting question. What is the probability that I would get it right just by guessing? Let's try August 17th.

Since Bernard wasn't sure of the month to start with he could not have been told the 18th or 19th since both of those days identify a unique month and Albert knows this also. So he was told the 17th (June or August) or the 16th (May or July) or 15th (May or August) or 14th (July or August). Since Albert also knows that Bernard wasn't told the 18th or 19th [or Bernard would have immediately known the month], Albert could not have been told June since June only has the 17th which is 'allowable'. Since Bernard knows that Albert knows [or at least we are assuming that], Bernard now knows that Albert was told August because if he had been told May or July, the question would still be undecided

 

[Deleted member 4993]

Interesting question. What is the probability that I would get it right just by guessing? Let's try August 17th.

Since Bernard wasn't sure of the month to start with he could not have been told the 18th or 19th since both of those days identify a unique month and Albert knows this also. So he was told the 17th (June or August) or the 16th (May or July) or 15th (May or August) or 14th (July or August). Since Albert also knows that Bernard wasn't told the 18th or 19th [or Bernard would have immediately known the month], Albert could not have been told June since June only has the 17th which is 'allowable'. Since Bernard knows that Albert knows [or at least we are assuming that], Bernard now knows that Albert was told August because if he had been told May or July, the question would still be undecided

That's a 0.

First think of Albert's response - he knows the month. His response says that it is not the month of May or June (which has the unique dates of 18 and 19).... and continue...

 

[Ishuda]

That's a 0.

First think of Albert's response - he knows the month. His response says that it is not the month of May or June (which has the unique dates of 18 and 19).... and continue...

Well I was working on it, highlight the part below the visible part of my post

 

[Deleted member 4993]

Agree with 1st half of Ishuda's "hidden!" reply.

BUT to me it has to be July, not August.
If Bernard told "14", he wouldn't know month (14 in both).

Since Albert now knows, he had to be told July,
else he wouldn't "now know" if he was told August,
since there are 2 days left in August: 15 and 17

So has to be July 16.

I think! Got a headache... Cruel puzzle

You got it.

 

[Ishuda]

Still not sure how to explain properly

With 5 days total in Jul/Aug and having to eliminate 4,
looks evident that it has to be 14's kicked out, then 15/17 Aug,
leaving 16 Jul, all associated with "now I know" and
"now I know too"...I'll let Ishuda handle that :cool:

It got to convoluted. I quit