It’s not often that a maths problem creates any sort of ruckus on the interwebs, but in the past day or so this little beauty has been causing a stir:
According to the Telegraph, it was part of a test given by the Singapore and Asian School Math Olympiads (SASMO) to high-achieving secondary school students.
If you don’t do a lot of logic puzzles it can be difficult to get started on something like this. When presented with this sort of problem I think the first instinct of many people is to engage their critical thinking skills to assess the integrity of the information presented.
Those are the same razor-sharp skills you use to ridicule the claims provided by the purveyors of breakfast cereal, toothpaste, and government policy.
Unfortunately, while those skills are indeed essential, they’ll get you precisely nowhere with logic puzzles. One of the core assumptions of logic puzzles is that the information is good. If something is presented as fact, it is indeed fact. Cheryl, Albert, and Bernard are all 100% honest and reliable. If Albert says he knows something then it’s absolutely true.
Additionally, and with all due respect to the SASMO, the wording of the question is a little confusing. Particularly those three lines of dialogue near the end. With that in mind, allow me to present…
The Strange Saga of the Unknown Birthday
by SASMO
with editing and dramaturgy from Steve the Math Tutor
Albert & Bernard have just become friends with Cheryl and they want to know when her birthday is. Cheryl, being a huge puzzle-fan, decides to have a little fun. She gives them a list of 10 dates, one of which is her birthday.
| May 15 | May 16 | May 19 |
| June 17 | June 18 | |
| July 14 | July 16 | |
| August 14 | August 15 | August 17 |
Then, separately, she tells Albert the correct month and Bernard the correct day.
Cheryl: Ok, without actually telling each other, figure out which one is my birthday.
Albert: Well, knowing the month hasn’t helped me. I don’t know when your birthday is. But I do know that Bernard doesn’t know either.
Bernard: Aha! I didn’t know her birthday at first but, now that you’ve said that, I do.
Albert: Aha! Now that you’ve said that, I know as well!
<Cheryl, Albert, & Bernard turn to the reader and fold their arms, smug smiles plastered across their honest, reliable faces.>
So when is Cheryl’s birthday?
Hopefully that wording makes the situation a little clearer. If you haven’t already seen and understood the solutions floating around online, have a go at it. I’ll work through the solution in the next post.