Albert and Bernard just became 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.
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?
Explain.
Solution to the Problem:
The answer is July 16.This question appeared on the Singapore and Asian Schools Maths Olympiads (SASMO) Test for 14-year-olds. But the question went viral after people across the world were left completely baffled. The problem, which tests logical reasoning, has been shared thousands of times online as people have tried to pose their best explanations of what at first appears to be an impossible question.
At first the question appears impossible to answer without a bit of extra information, but we know Cheryl has already told Albert the month of her birthday, and Bernard the day.
Each of the men does not know what the other has been told.
This allows a reductive reasoning to be used to begin to whittle down the number of options.
So, firstly, for Albert to be 'certain' that Bernard cannot know the answer - as suggested in the first statement he makes - we can deduct that the birthday is not in May or June.
This is because in the months of May and June there are numbers (dates) that only occur once across the four months - namely May 19 and June 18.
If Albert had been given May or June as the month, there is no way he could be certain that Bernard doesn't know the birthday. Bernard, after all, might have been the number 18 or 19.
For Albert to be 'certain' that Bernard doesn't know, Albert must have been given a month that does not contain one of these 'unique' dates - i.e. July or August.
Albert's disclosure now gives Bernard the clue he needs, and says he now knows the birthday.
Bernard only knows the number of Cheryl's birthday, but from Albert's statement he has now also ruled out both May and June. This is because he realizes Albert has ruled out May and June because of the 'single number' aspect above.
So there are now just five remaining dates - July 14, July 16, Aug 14, Aug 15, Aug 17 - and Bernard says he knows which is the birthday.
Because he now knows the date, we can whittle it down further to three dates by ruling out the numbers that appear in duplicate.
One Facebook user's explanation for how to solve the taxing maths' problem is shown in the image above.
If Cheryl had told Bernard that her birthday fell on the 14th of the month, then he could not have worked out the date at this stage.
However, as he states that he now knows the date, we can rule out July 14 or August 14.
This leaves just three dates to chose from - July 16, Aug 15 and Aug 17.
Following Bernard's statement, Albert is then apparently able to deduce the date of Cheryl's birthday.
This means her birthday must be the only remaining date in the month he was originally told. Given that there are two dates left in August and one in July, it has to be the July date.
So the answer is July 16.
The problem was posted on Facebook by 'Hello Singapore' television presenter Kenneth Kong, and went viral as people posted their various solutions to the problem.
It was set for 14-year-olds in the Singapore and Asian Schools Math Olympiads (SASMO), which were held on April 8.
This year around 28,000 students from countries across the world including Singapore, Thailand, Vietnam, China and the UK took the test.
Henry Ong, executive director of SASMO, told Mothership.sg: 'Being Q24 out of 25 questions, this is a difficult question meant to sift out the better students. SASMO contests target the top 40% of the student population and the standards of most questions are just high enough to stretch the students.'
Of course, perhaps the more important question is whether Cheryl deserves a birthday gift at all after putting us through all of this.
Correctly solved by:
| 1. Gage Covington |
Mountain View High School, Mountain View, Wyoming |
| 2. Keith Mealy | Cincinnati, Ohio |
| 3. Morganne Johnson |
Mountain View High School, Mountain View, Wyoming |
| 4. Tristan Hamblin |
Mountain View High School, Mountain View, Wyoming |
| 5. perryc@kpmath.com |
Mountain View High School, Mountain View, Wyoming |
| 6. Caiden Lawrence |
Mountain View High School, Mountain View, Wyoming |
| 7. Keagan Genzer |
Mountain View High School, Mountain View, Wyoming |
| 8. Cierra Snow |
Mountain View High School, Mountain View, Wyoming |