Updated 16 April 2015

The almost impossible grade 8 maths question answer

The answer to the maths problem from a Singapore that nobody can solve, even though it's meant for 14-year olds.


Brain scrambled? Don't worry, you aren't the only one. Fortunately, we've got the answer, unfortunately, it's almost as complicated as the question.

N.B. If you have no idea what we're talking about, you can read the question here.

So, there are three lines to the answer, and we'll go through each one to find out when Cheryl's birthday really is. Remember that this is a purely logical and mathematical exercise, aspects like why Cheryl is so unnecessarily obtuse about telling people when her birthday is don't come into it.

The ten possible dates are:

May 15 — May 16 — May 19

June 17 — June 18

July 14 — July 16

August 14 — August 15 — August 17

Line one

Albert says: "I don’t know when your birthday is, but I know Bernard doesn’t know either."

The first part of this is useless, we know that Albert doesn't know when the birthday is, so you can ignore that, but how can Albert know that Bernard doesn't know? The question really is: how could Bernard know, given that he only knows the day? There is one way. If Cheryl had whispered either 18th or 19th into Bernard's ear he would immediately know the date of her birthday because those days only appear once, the 19th May and the 18th June.

Therefore, the only way Albert can be certain Bernard doesn't know when the birthday is if he knows the birthday isn't in May or June, therefore Cheryl must have told Albert that her birthday is in either July or August, this removes half of the possible answers.  

Line two

Bernard says: "I didn’t know originally, but now I do."

So, after hearing Albert speak, Bernard is now able to deduce when Cheryl's birthday is. He has also realised that it isn't in May or June. Now, with just the day, he can figure out which month it is in. This means that the day he was given is not the 14th, as that appears in both months and he would not be able to deduce which one. Thus, he must have been told either the 15th, 16th or 17th. As each of these days only fits into one month, that is the answer, but we're not done yet.

Line three 

Albert now says: "Well, now I know too!"

There are now just three possible dates 16th July, 15th August, 17th August. If Cheryl had told Albert her birthday was in August, he wouldn't know for certain as there are two possible dates in August, therefore, if Albert knows, July is the only month remaining.

Cheryl's birthday is on the 16th July. 

Did you get it right? Do you even understand the answer? Let us know in the comments!

Image credit: Maths by Shutterstock


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