Can you solve this mind-bending maths problem given to Singapore schoolchildren?

Mon, 13 Apr, 2015 - 16:01

Dave Molloy

A maths problem given to Singapore's schoolchildren has gone viral globally, after a TV personality posted it to his Facebook page and left grown-ups tearing their hair out.

Kenneth Kong, a presenter from Singapore TV, posed the question claiming it was for children aged around 10.

Stunned by the difficulty, people set about solving it for themselves - but it's a little trickier than you might expect.

The problem was actually set for children around 14 years old - and those who are competing in the Singapore and Asian Schools Maths Olympiads, at that. The post became so popular that the director of the maths Olympiads wrote to Kong to ask he clarify the difficulty.

But it's a logical puzzle that doesn't require any actual arithmetic to solve.

Can you answer it?

The problem

Albert and Bernard just become friends with Cheryl, and they want to know when her birthday is. Cheryl gives them 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. [Clarification: this means Albert is told only the month, Bernard is told only the day.]

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?

Try and solve it yourself before you scroll further - the solution follows just below.

The answer

This problem is all about the process of elimination.

Albert knows the month but not the day. But he tells us that Bernard can't possibly know either.

So Bernard can't know that it is the 19th or 18th - because they're only in one month and he'd know instantly what month it is. So it has to be a repeated date, not one that appears only once.

So we throw away May and June as options.

Next, Bernard says he didn't know - but now he does. So Albert saying it can't be May or June has left him with a way to figure out the right answer.

That means the date Bernard was told has to be the only remaining date that doesn't repeat from either July or August. Otherwise he'd never figure it out. Only one date fits that description.

July 16 is the answer.

In real life, of course, the answer would be that Cheryl is probably not a whole bunch of fun to hang out with, and Albert and Bernard go play elsewhere.