The Math Question That Went Viral

The Atlantic ^ | April 14, 2015 | Terrence F. Ross

[QT3.14]

One word problem from a Singaporean school exam briefly became the talk of the Internet last weekend....[Snip]... The puzzle went viral across the country, with people ranging from perplexed adults to eager teenagers grappling with the simple question: "So when is Cheryl's birthday?"

[Don Corleone]

Who killed Laura Palmer

Who shot JR?

Is the truth really out there?

"At this point what does it matter?"

[boomstick]

To finish up, the fact that Bernard knows tells Albert that it’s the 15th (Aug), 16th (Jul), or 17th (Aug). Albert knows the month — if it were August, then he still wouldn’t know which day, but if he knows July then there’s only one possible day (the 16th, therefore July).

[BlackAdderess]

Excellent :)

[WayneS]

July 16

[central_va]

[RightOnTheBorder]

July 16th

Albert(month) knows Bernard(day) cannot know. This means that Albert knows the month does not contain a unique date thus eliminating May and June. Once Bernard knows May and June are out then the date he knows gives him the answer. Since the date must be unique to July or Aug, the 14th is out. If the 14th is out and Albert now knows the answer that means that his month was July because if the month was August he would still have two choices and couldn’t be sure.

[RoosterRedux]

By Albert saying he knows Bernie doesn't know, he's saying that the month is not one containing a single date. I.e. not May 19 or June 18.

So this tells Bernie that Albert, knowing only the month, has just eliminate all May and June and leaves July and August.

By announcing that he now knows the correct birthday, Bernie is saying that it is obviously NOT July 14 or Aug 14 because if all Bernie had was the day 14, there would be 2 possible choices.

That leaves July 16, Aug 15 and Aug 18.

For Albert to announce that he now knows Cheryls birthday, that tells us the the birthday is July 16.

If it were the 15th or 17th, that would leave Albert without knowing the precise month, since there 2 August possibilitIes.

Therefore, July 16th is the birthdate.

[BitWielder1]

July 16.
18 and 19 can be ruled out because then Bernard would instantly know the answer.
Since Albert knows for a fact that Bernard does not know, it rules out May and June.
If it was 14, Bernard would still not know, but he does now, so it's either 15, 16, or 17.
If it was 15 or 17, then Albert would still not know, but he was able to figure it out, so it must have been 16. July 16.

[Fido969]

July 16

[sten]

if bernard knows, then the numbers that are ambiguous must be removed.

the 14th can be either july or august... so remove it.
the 15th and 17th are both august... so remove it.

that leaves the 16th of july

[BitWielder1]

Dang, sten beat me to it. Congrats sten.

[RoosterRedux]

I like your logic (I think), but I keep arriving at July 16.

[RoosterRedux]

Nicely put...and correct.

[FredZarguna]

Here's the logic: On the basis of Albert's statement that Bernard cannot know the answer, you can rule out any month with a unique day; because if Bernard were holding [May] 19 or [June] 18 he could know the Birthday without any information from Albert. Albert knows B cannot know this. Therefore we know that Albert is holding July or August.

Now Bernard says he knows the answer, which means Bernard now knows the month. That is only possible if the day Bernard is holding is the 16th. If it's the 14th, Bernard would only know that Albert had either July or August -- which tells him nothing new, since he already knew that on the basis of what Albert said. The only way out is July 16th.

Now knowing that Bernard knows, Albert knows what we know, so he knows as well.

[Ray76]

I’m a little doubtful about how Bernard makes his claim, but Alert’s claim confirms the answer.

Albert and Bernard each have been given correct data.

Albert was given the month but, as there are multiple possibilities within each month, he can not determine the date.

Bernard was given the day. Possible days are: 14, 15, 16, 17, 18, and 19. Except for 18 and 19 there are multiple occurrances of each day.

Albert announces that he knows that Bernard can not know the date. This tells Bernard that the day is not unique. Therefore May 19 and June 18 can be ruled out.

Bernard said “at first I didn’t know, but now I do”.

At first his information, the day, was not unique.

At first Albert’s information, the month, was not unique.

But now after Albert’s announcement and consequent ruling out of May 19 and June 18 Bernard claims to know the answer. Then Albert, who knows only the month, says he too knows. The only month left with a single day is June. Albert’s claim can only be supported if June 17 is the answer.

That’s my story and I’m sticking to it. ;)

[ml/nj]

July 16

Albert must have either July or Aug to know that Bernard doesn't know right off the bat, which he would if the birthday were either May 19 (the only 19) or June 18 (the only 18).

It cannot be the 14th because Bernard would still have to choose between July 14 and August 14. So Bernard knows it is either July 16, if he was told 16, and similarly he would know it was August 15 or August 16 if he was told 15 or 16.

But Albert still wouldn't know if he were told August, so he must have been told July. And among the three possibilities that Bernard might know only one is in July; July 16.

ML/NJ

[FredZarguna]

The correct answer is July 16.

[Ray76]

You know this for a fact?

[FredZarguna]

Yes. I proved it at post #74. So have several others on this thread.

[sphinx]

We aren’t given her race, sexual preference, or handicapped status, so we can’t possibly answer the question.