Solving the viral Singaporean math problem

The following problem has become very popular in social media:


In this blog we have solved similar problems before, but this is one that can be easily solved by hand. We only need to be careful not to confuse our knowledge state with the one of Albert & Bernard.

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.

We will describe a list of the possible knowledge states of Albert and Bernard after being given that information:

  1. May 15 or May or May 19
  2. June 17 or June 18
  3. July 14 or July 16
  4. August 14 or August 15 or August 17
  1. July 14 or August 14
  2. May 15 or August 15
  3. May 16 or July 16
  4. June 17 or August 17
  5. June 18
  6. May 19

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

We already knew that Albert wouldn’t know the day based just on being given the month, but he is giving us additional information by telling us that he knows that Bernard doesn’t know. Bernard would know the date if the day were 18 or 19, so Albert knows that those days could not be the right ones. That excludes options 1 and 2 from our knowledge of Albert knowledge:

  1. July 14 or July 16
  2. August 14 or August 15 or August 17

Bernard can do the same deductions we have and eliminate the options that are not possible from his state of knowledge (all the options with months different from July and August).

  1. July 14 or August 14
  2. August 15
  3. July 16
  4. August 17

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

Updating our knowledge of Bernard knowledge:

  1. August 15
  2. July 16
  3. August 17

As Albert also knows what we know about Bernard knowledge…

  1. July 16
  2. August 15 or August 17

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

Now we know the right date:

  1. July 16
  1. July 16

2 thoughts on “Solving the viral Singaporean math problem

  1. Nice and concise explanation!

    I think the way i approached this riddle is overly complicated. For instance, for the first statement by reasoning was something like “June and May have unique days, if Albert’s month was one of those then he couldn’t be certain about Bernard not knowing the birthday, therefore the month must be one of July or August”.

    The logic is equivalent, but all those negations make me feel like my approach to this kind of problem solving could be much simpler. Did you solve the riddle using the reasoning described in the post, or is that a distilled version of a more involved original solution?

  2. mchouza says:

    Thank you for your comment!

    I solved the problem while I was writing the post, without having to backtrack… but that was mostly due to its similarity with the product & sum riddle (I did my cleanup there, so to speak 😀 ).

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