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Cheryl's birthday

RogerS

RogerS

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I know how you chaps like a challenge.

The teenage maths test
Albert and Bernard want to know when Cheryl’s birthday is. Cheryl gives them ten 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 the month in which her birthday falls, and she tells Bernard the day’s number.

Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.

Bernard: At first I didn’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?
 
RogerS":3lv1vobo said:
I know how you chaps like a challenge.

The teenage maths test
Albert and Bernard want to know when Cheryl’s birthday is. Cheryl gives them ten 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 the month in which her birthday falls, and she tells Bernard the day’s number.

Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.

Bernard: At first I didn’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?
Click to expand...

I take it you are back on the beer again.

I'm with Paul and I had a headache already.
 
OK, how is this:

RogerS":3c8o99yn said:
I know how you chaps like a challenge.

The teenage maths test
Albert and Bernard want to know when Cheryl’s birthday is. Cheryl gives them ten 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 the month in which her birthday falls, and she tells Bernard the day’s number.

Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.
Click to expand...

If Albert knows that Bernard doesn't know, then it cannot be on a date that is only present in 1 month. Thus it cannot be May 19 or June 18, since if Bernard was given the numbers 18 or 19 he would know which of the 10 possible dates it had to be. If it cannot be those dates and Albert still doesn't know which day is Cheryl's birthday, then it must be in a month that has two possible choices left. As a consequence it cannot be June 17th.

Bernard: At first I didn’t know when Cheryl’s birthday is, but I know now.
Click to expand...

We are currently left with 7 possible dates. If Bernard (who is given the date, not the day) now knows when it is, only 1 of the 7 dates is unique - there are two 14's, two 15's, two 16's and one 17. Thus Bernard must have been given the number 17 to know when Cheryl's birthday is.

Albert: Then I also know when Cheryl’s birthday is.
Click to expand...

If Albert has eliminated June 17th already ,and Bernard now knows, then Cheryl's Birthday must be August 17th.

Don't know if this is right, but it seems logical......

Steve
 
Good logical thinking, Steve.

At least at the beginning :D

So Albert knows the month, and every month has more than one possible date, so of course he doesn’t know when her birthday is.

The only way that Bernard could know the date with a single number, however, would be if Cheryl had told him 18 or 19, since of the ten date options only these numbers appear once, as May 19 and June 18.

For Albert to know that Bernard does not know, Albert must have been told July or August, since this rules out Bernard being told 18 or 19.

...........
 
Yep, so ....

When Albert says he knows Bernard doesn't know the date, Bernard realises that the only way Albert could know that for sure is if the month wasn't one with any unique dates. This eliminates May and June as possible months. Seeing this, Bernard(knowing the day) now knows the month as well.

When Bernard says he now knows the date, Albert realises that for Bernard to know the date, that the day can't be the 14th(since it occurs in both July and August). Now the only dates left are July 16th, August 15th and August 17th.

Now Albert knows the date and since he only knew the month, but not the day, the only possible date would have to be July 16th because if the month was August then Albert wouldn't be able to find the day because there would be two possible answers instead of one.
 
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