Video

When Is Cheryl’s Birthday?

Solving a logic problem that spread around the world.

When, exactly, is Cheryl’s birthday? A charming logic puzzle led to much hand-wringing over this question in the past week. A prompt about two men, Albert and Bernard, trying to figure out a woman’s birth date with limited information spread from a Singapore math competition to social media around the world. Below, read the original puzzle, then watch our video explanation of the solution.

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.

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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.

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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?

Here’s how to figure it out, with one simple chart:

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See? That wasn’t so bad.

And if you are the type of person who would rather be told the answer than shown, here’s a bonus way to think about it for Clue players, courtesy of Paul Smith, a developer for Slate’s Panoply:  

The solution becomes clear when you translate Cheryl’s clues into Clue-speak:  

May = Library

June = Conservatory

July = Dining Room

August = Ball Room

14 = Mrs. White

15 = Col. Mustard

16 = Professor Plum

17 = Miss Scarlet

18 = Mr. Green

19 = Mrs. Peacock

Suspects seen in …

The Library: Col. Mustard, Professor Plum, Mrs. Peacock

The Conservatory: Miss Scarlet, Mr. Green

The Dining Room: Mrs. White, Professor Plum

The Ball Room: Mrs. White, Col. Mustard, Miss Scarlet

(Albert knows the room and Bernard knows the killer.)

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Albert says Bernard can’t win Clue. This means the mystery can’t be solved only by knowing the killer. So, the room can’t be the Library or Conservatory—if it were, Bernard would potentially be able to solve the mystery if the killer were Mrs. Peacock, who was in the Library all evening, or Mr. Green, who was only ever in the Conservatory.

But because Albert blurts out that he knows Bernard can’t know, Bernard can now eliminate the Library and Conservatory. And then Bernard blurts out he now knows, which means that Albert now knows. Bernard must have eliminated Mrs. White, who both know was lurking in both the Dining Room and the Ball Room—if she’d done it, it would be impossible for Bernard to know which room she did it in. Since Albert figured out the killer, that means the murder must have been in the Dining Room, because if it had been in the Ball Room, Albert wouldn’t have been to tell if it was Colonel Mustard or Miss Scarlet, who were in there together.

Professor Plum did it in the Dining Room, clearly.

Update, April 15, 2015: This post has been updated to clarify the language in the Clue explanation.

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