December 4, 2018

Okay, so here’s that one question to fool them all! Logic should be common sense, and common sense should be common, right?

But a Math problem created to test the logical reasoning skills of 14-year-olds in the Singapore and Asian Schools Math Olympiad, in April 2015, is actually leaving people from all over the world baffled.

The question in question … er, the problem at the center of all the ruckus has been shared thousands of times online. And people from all over have tried to give their best explanations to the “impossible question.” But there is logic to this madness. Remember to be reasonable when you attempt to crack it.

Posted by Singapore and Asian School Math Olympiad on Monday, April 13, 2015

The Question:

Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of ten possible dates: May 15, 16, 19; June 17, 18; July 14, 16; or August 14, 15, and 17. Cheryl then tells Albert only the month and Bernard only the date.

Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know either.

Bernard: At first I didn’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?

Figuring It Out:

At first, this seems impossible to work out without more information. Well, logic dictates it’s a question that expects you to use a process of elimination, and that the information given is enough to figure out the answer. The answer cannot be “impossible” to figure out through the facts. Otherwise, any answer is correct because the question is flawed to start with.

So, let’s look at the logical process used to answer the question: Out of all the dates, only the numbers 18 and 19—which fall in June and May respectively—occur once. But the fact that Albert knows that Bernard does not know the birthday means Cheryl must have told Albert that her birth month is either July or August.

So, Bernard’s date was not unique with all the months included; therefore, he says that he didn’t know Cheryl’s birthday initially. But after Bernard discards May and June, he comes across the fact that the remaining set of exclusive dates has the number 14 occurring twice. After he eliminates July 14 and August 14, he’s left with only three possible dates: July 16, August 15 or August 17.

Therefore, Bernard later on says now he knows. Why?

By this time they both realize the month Cheryl has told Albert must be unique too, which eliminates August from the last three options. Therefore, Albert says he knows Cheryl’s birthday for sure. The month he has been told must be July, which has only one unique date. The answer is July 16.

Posted by Singapore and Asian School Math Olympiad on Monday, April 13, 2015