When is Cheryl’s Birthday?

Photo acquired from Wikimedia Commons, the free media repository

Birthdays are a fun tradition that you get to celebrate with your friends and family once a year…that is, if you tell them when your birthday is.  In a logic puzzle that has been making the rounds on the Internet, Cheryl tells her new friends Albert and Bernard her birthday in a very unusual manner.


The puzzle goes as follows:

Albert and Bernard just become friends with Cheryl, and they want to know when her birthday is.  Cheryl gives 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 does not know too.
Bernard:  At first I don’t know when Cheryl’s birthday is, but I know now.
Albert:  Then I also know when Cheryl’s birthday is.

So when is Cheryl’s birthday?

This puzzle was part of the Singapore and Asian Schools Math Olympiads (Sasmo), aimed at students around 15 years old.  At first, it was reported that this problem was given to 11 year old students, which prompted an outcry about the unreasonable difficulty of standardized tests.  However, once it became clear that the question was aimed at older students, the focus reverted back to the interesting logic behind the problem.  Henry Ong, Sasmo’s executive director, showed the purpose of the problem by explaining that

[There is] a place for some kind of logical and analytical thinking in the workplace and in our daily lives.

A full video explanation of the problem solution can be found here:  Cheryl’s Birthday: Singapore’s maths puzzle baffles world.

In case it wasn’t enough of a challenge to figure out when Cheryl’s birthday is, check out this Transfinite Epistemic Logic Puzzle that she, Albert, and Bernard played as a party game!

About Stephanie Blanda

Stephanie is a math Ph.D. student, with a minor in Computational Science, at Penn State University. She obtained a B.S. from Lebanon Valley College, where she double majored in Mathematics and Computer Science. Currently, Stephanie is studying the interface of two viscous fluids under a shear flow, specifically with applications to wind generated ocean waves.
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