Trinity_Test_Fireball_16ms_lq.jpg

SASMO stands for "Singapore and Asian Schools Math Olympiad". According to its webpage it is an organization devoted and dedicated to bringing a love for Mathematics to students. It has to do with interest and enthusiasm for mathematical problem solving, developing mathematical intuition, reasoning and logical thinking, as well as creative and critical thinking. The following problem, aimed for students between 14 and 16, was proposed by SASMO and quickly went viral through the social networks. It is known as the Cheryl's birthday problem.

Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 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 and Bernard separately the month and the day of her birthday respectively.

Albert: I don't know when Cheryl's birthday is, but I know that Bernard doesn't know too.
Bernard: At first I don't [sic] know when Cheryl's birthday is, but I know now. [A better grammar could be: At first I didn't know when Cheryl's birthday was, but now I do]
Albert: Then I also know when Cheryl's birthday is.
So when is Cheryl's birthday?"

It's not difficult to get the answer if you are used to these kind of problems, but if this is the first time you are facing one of them, it is likely that you have to think about at it for a long time. I hope you enjoy it. 

You got it? Ok, here you have the key points that you should have followed in your reasoning:

• The first comment of Albert eliminates all the dates of May and June. Do you see why?

• The following comment of Bernard eliminates July 14 and August 14. 

• The last comment of Albert eliminates August 15 and August 17. 

So the final answer is... exactly, the remaining date you thought, didn't you?

By the way, the photo we have chosen for this post is not a birthday cake but a nuclear bomb explosion... Are you any good at History of Science?

 

REFERENCES:

- http://mathsolympiads.org

- http://gaussianos.com/explicacion-del-problema-del-cumpleanos-de-cheryl/

- http://www.nytimes.com/2015/04/15/science/answer-to-the-singapore-math-problem-cheryl-birthday.html

- https://en.m.wikipedia.org/wiki/File:Trinity_Test_Fireball_16ms.jpg

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