There has been a logic question from Singapore that has gone viral. You have likely heard of the math problem involving Cheryl, Albert, and Bernard. If not, here’s a recap below.

The Problem

The Answer

It’s a tricky puzzle to solve and has stumped many mathematicians and scholars. Alex Bellos, of the Guardian set out to solve the puzzle and so did we. Both of us arrived at the same answer; here’s how.

Firstly, we know Albert is told the month of Cheryl’s birthday. This means her birthday is either in May, June, July, or August.

Cheryl tells Bernard, the day of her birthday. This means she is born on either the 14th, 15th, 16th, 17th, 18th, or 19th out of the four months.

We broke it down, line by line.

Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know too.

This is a redundancy. Because Albert only knows the month, and every month has many days, therefore it’s impossible for Albert to know Cheryl’s birthday.

There are only two number options that appear once, May 19 and June 18, out of the ten options given in the problem. It’s possible for Bernard to know the date with a single number, but that would mean Cheryl told him either 18 or 19.

In order for Albert to know that Bernard doesn’t know, the month must be either July or August, which nixes Bernard being told either the 18th or 19th.

Bernard: At first I don’t know when Cheryl’s birthday is, but now I know.

Bernard reasons that Albert has been told either July or August. If Bernard knows Cheryl’s complete birthday, the number he was told must have been the 15th, 16th, or 17th, all of which refer to a specific month. If Cheryl had told Bernard the 14th, he would be unable to determine wether Cheryl’s birthday was in July or August, as the number 14 is repeated.

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

For Albert to know when her birthday is, he must have been told July. Because of Bernard’s previous statement, Albert has concluded that the possible dates are July 16th, August 15th, and August 17th. If Albert had been told August, he would still be uncertain as to which day was her birthday.

Therefore, the answer is July 16th.

BUT IS IT?!

There has been some debate about the possible answer to this logic problem. Some are even calling it the math version of #thatdress. Why? Because it has many possible answers. James Grime of The Guardian, a colleague of Alex Bellos’, decided to riddle out what it is about this logic problem that’s stumping even the most accomplished mathematicians. Here is a summary of his findings.

Depending on how you work out this problem, you may arrive at another answer. That answer is August 17th, and here is why.

Let’s break this one down too.

To start, Albert states he knows that Bernard does not know Cheryl’s birthday either. He figures that Bernard cannot have been given a unique date, being 18 or 19. He then teases Bernard, saying he does not know the answer either. This is the first line of the conversation.

As such, Bernard learns that Albert has learned that Bernard does not have a unique date. Bernard deduces that if Albert had been told June, he would know the answer because the only date left is June, the 17th. Therefore, Bernard knows the month is not June and claims to know the answer. This is the second line of the conversation.

Because Bernard is so confident he knows the answer, he must have a unique date that is not the 18th or 19th. Every other date is doubled, two 14ths, two 15ths, two 16ths, and two 17ths, but because Bernard has ruled out June 17 as an option, that leaves a unique date of August 17th.

Albert reasons the problem from Bernard’s perspective, and arrives at the same answer. This is the third line of the problem.

Therefore, August 17th is another possible answer.

But how are two answers possible?

The key is in how you interpret the first line of the problem. If Albert is guessing Bernard doesn’t know (deduction), then we arrive at the July 16th answer. If Albert is certain that Bernard doesn’t know the answer (statement of fact) then we arrive at August 17th.

The quiet shift between deduction and fact changes the entire nature of this logic question. By assuming the first line is fact, the reader can riddle out the problem from that statement alone. However, if the first statement is not assumed as fact, the remaining lines of the conversation become instrumental to solving the puzzle.

HOWEVER, the creators of the problem, the Singapore and Asian School Math Olympiads, have rejected this possible answer. They claim that we cannot assume what Bernard doesn’t know as fact.

So it would appear that the true answer is July 16th. Just like that dress was really black and blue.