Cheryl's Birthday

Cheryl's Birthday puzzle

This popular logic puzzle was originally set for Singaporean maths students, since being posted on Facebook by a teacher in Singapore, it has generated much debate!

Question:

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 seperately the month and the day of her birthday respectively.

Albert: "I don't know when Cheryl's birthday is, but I know that Bernard can't know for sure yet either"
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?

Answer: (click to show)

Recap: We have three statements made in order, Albert knows the month only, Bernard knows the day only.

If Bernard was told that the day was the 19th or 18th, he would know the whole birthday as these are unique. The first statement tells us that the month must be either July or August. If Albert had been told that it was one of these months, then he wouldn't know for sure that Bernard doesn't already know the whole date.

So the month is July or August.

The second statement, made by Bernard, tells us that he now knows. That means that the day must be unique within July and August. So the 14th is not an option.

The three dates left are: July 16, August 15, August 17.

The last statement, made by Albert, tells us the birthday. If it was one of the August dates then Albert wouldn't know the date because there are two to choose from. This tells us that Cheryl's birthday is July 16th .