4.2. Cheryl’s birthday problem goes viral


SASMO stands for “Singapore and Asian Schools Math Olympiad”. According to its webpage it is an organization devoted and dedicated to bringing a love of Mathematics to students. It concerns itself 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 at students between 14 and 16, was proposed by SASMO and quickly went viral. It is known as 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 [sic, although better grammar would be 'either' instead of 'too'].

Bernard: At first I don't [sic] know when Cheryl's birthday is, but I know now [sic, but better grammar could be: 'At first I didn't know when Cheryl's birthday is, but now I do'].

Albert: Then I also know when Cheryl's birthday is.

So, when is Cheryl's birthday?

It could seem impossible (§1, §4, §30) to solve the problem with apparently no information provided, but it isn't if you are used to these kind of problems. However, if this is the first time you are facing one of these, it is likely that you have to think about 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:

• Albert's first comment eliminates all the dates of May and June. Can you see why?

• Bernard's following comment eliminates July 14 and August 14.

• Albert's last comment eliminates August 15 and August 17.

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