# When Is Cheryl’s Birthday? This Singapore Math Question For Kids Is Going Viral

These days, math questions from around the world are going viral on the internet. One such question is on Cheryl’s birthday.
The math problem first showed up on
Facebook when a Singaporean television host ‘Kenneth Kong’ shared it. People have been attempting to sort Cheryl’s birthday ever since.

This is the exact text of the question:

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?

—————–

It was later discovered that the math problem was meant for high school students for an upcoming math olympiad. So can you give us the correct answer? Let us know in the comments section!

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There is still one thing that Bernard and Albert don’t know that only Cheryl know. The year of her birthday. Here are the choices:-

500 B.C.
300 B.C.
100 B.C.
2005

It’s July 16th:

We start off with 10 dates:

May 15 May 16 May19
June 17 June 18
July14 July 16
Aug 14 Aug 15 Aug 17

Albert knows that Bernard does NOT know the birthday therefore it cannot be May 19 or June 18 since these are the only 2 which are unique numbers.

May 15 May 16
June 17
July14 July 16
Aug 14 Aug 15 Aug 17

Bernard knows that Albert only knows the month so Bernard also knows that May and June are ruled out.

July 14 July 16
Aug 14 Aug 15 Aug 17

B now says that he knows the birthday for sure and we know that he only has one number.

We can rule out 14 since it appears in 2 months

July 16
Aug 15 Aug 17

A now has the knowledge that B knows exactly which date is the birthday so his number helped him identify an exact month.

A knows it must be July 16th since August has 2 possibilities and July only one possibility

It must be July 16th

It’s July 16th. Break it down. The only way Albert would know that Bernard didn’t know her birthday is if he knew that she didn’t give him the number 18 or 19 (as he would then know it was May 19th or June 18th). The only way he’d know that is if she gave him neither June or May. Now Bernard knows that it’s either July or August and because of that knows the date therefore Albert knows he couldn’t have the number 14 as that could be July or August 14th meaning he still wouldn’t know. Now the only possible dates are July 16th, August 15th or August 17th. The only way Albert would know the answer is if he was given the month of July as if he was given the month of August he wouldn’t know if it was the 15th or 17th.

From their perspectives:

Albert was given July.
Bernard was given 16
Albert knows Bernard has 14 or 16 so can’t have 18 or 19 and know the date.
Bernard knows Albert knows he can’t have 18 or 19 so it must be July or August therefore July 16th
Albert knows that Bernard can’t have 14 as he wouldn’t know if it was August or July 14th so he must have 16.
They both know the date is July 16th.

When Albert says that he knows that Bernard does not know he is also saying that it is not May or June. Why? both May and June has unique dates in them, 18th and 19th, so had it been either of those months Albert couldn’t have said what he said. When Bernard learns that it’s not May or June he obviously knows the date since he knows the day. Since Albert knows it’s July he also know it’s 16th since it couldn’t have been 14th because that day is repeated i August. Had it been August, Albert wouldn’t have known, since that month has three two days in addition to the 14th.
16th July, QED. by the elimination method.

It’s August 17
first of all Cherry ask them “Can you figure it out now?” that mean that she have not whispered to Bernard the number 18 or 19
Then Albert have :
May 15, May 16, May 19
June 17, June 18
July 14, July 16
August 14, August 15, August 17
If Cherry had told him “June” he would been able to say June 17, so that one is out to and he still can not determent the birth day and say “I don’t know when your birthday is, but I know Bernard doesn’t know, either.”
Now Bernard have :
May 15, May 16, May 19
June 17, June 18
July 14, July 16
August 14, August 15, August 17
He say that now he can determent the birthday, and the only number that is not double is 17,

May 19. Bernard only knows the day, so if he was able to figure out the birthdate it must be May 19th since that is the only day that has no other Month attached to it. And, if Albert knows that Bernard was able to figure it out while only knowing the day, and he knows the month, he will know it must be May 19th since it’s the only choice for Bernard.

It can’t be May or June because they both have exclusive dates (19th and 18th), and seeing as Albert KNOWS that Bernard doesn’t know, it has to be either July or August. (e.g. If Al was told ‘May’, then Bern could have been told ’19’ and would instantly know her birthday, therefore breaking rule #1)

Plot twist….. None of these date’s are correct. Cheryl actually didn’t like ether of them and wanted to throw them off.

19 and 18 are not repeated, therefore these days are possible. Now knowing one of these dates, without knowing the month is not possible. since June appears 2 times and May appears 3 times, therefore May is most probable. So the answer is May 19…

My logic: It has to be a number that can ONLY be known, with the knowledge that
1. Al doesn’t know.
2. Al knows Ber doesn’t know it.
3. Once it was said, then, Ber knows it.
and finally, 4. While Ber may know it, because he was given a second hint, (the actual day) we do not.