When Is Cheryl’s Birthday? The Math Problem Gone Viral…Can You Figure It Out?

Trivia

The internet is full of wonders; a mesh of information ranging on topics as diverse as literature to healthcare to the universe, one can find everything on the interconnection of networks aka ‘internet’. Recently a mathematics question that was apparently solved by fifth-graders in Singapore baffled the internet paparazzi.

The question was originally posted on the social media site Facebook, by a television anchor based in Singapore named Kenneth Kong.

Photo Credit: http://www.nytimes.com/2015/04/15/science/a-math-problem-from-singapore-goes-viral-when-is-cheryls-birthday.html?_r=2

Photo Credit: http://www.nytimes.com/2015/04/15/science/a-math-problem-from-singapore-goes-viral-when-is-cheryls-birthday.html?_r=2

The question grabbed a lot of eyeballs and suddenly everyone was trying to figure out when is Cheryl’s birthday. Though one would wonder if it was heights of mystique on part of Cheryl that she gave the two boys a piece of puzzle to figure out her birthday.

The New York Times decided to rephrase the confusing question for their readers and here’s an alternative for the original question. Though the presentation is different, the inherent logic of the question is intact in the reworded version.

“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?”

Apart from figuring out Cheryl’s birthday, the netizens were also involved in a debate over the standard of education in Singapore. While many were surprised others even expressed their concern over the fact that students in fifth-grade shouldn’t be burdened with such an extensive curriculum.

But later it was verified that the question was asked in a Math Olympiad organised for high school students.

Still wondering if you can beat those high-school studs from Singapore? If you’re clueless or going nuts over Cheryl’s birthday, read onto find the solution.

Arranging the list of dates in a table obviously helps.

May 15 16 19
June 17 18
July 14 16
August 14 15 17

Albert says: I don’t know when your birthday is, but I know Bernard doesn’t know, either.

Assuming everyone is telling the truth, from the first half of the sentence we deduce Albert knows the month and Bernard knows the day.

The trick lies in thinking how Albert could be sure that Bernard doesn’t know. This implies Cheryl did not whisper 19 to Bernard as there is only one month with the date. Similarly we can conclude that Cheryl’s birthday is not on 18.

But if the above were true, it would also imply that Cheryl did not whisper May or June to Albert, as Albert himself says he does not know the exact date. Thus we can eliminate half the possibilities.

Then considering Bernard’s reply: I didn’t know originally, but now I do.

As we had earlier concluded that the only probabilities we are left with include – July 14, July 16, Aug. 14, Aug. 15 and Aug. 17.

Now thinking how could Bernard know, we realise that Cheryl definitely did not tell him 14, as then there he would be left with two choices July 14 and Aug 14.

So now we have only three possible correct dates: July 16, Aug. 15 and Aug. 17.

Now Albert says: Well, now I know too!

From this we conclude that Cheryl did not mention August to Albert as then he would have to decide between two possibilities – Aug 15 and Aug 17.

Thus we zero in on July 16, as the date on which Cheryl’s birthday falls.

If you had fun solving this riddle, then do share with your friends to double the fun.

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