# Puzzle 51| Cheryl’s Birthday Puzzle and Solution

**(Wiki) ****Cheryl’s Birthday** is the unofficial name given to a mathematics brain teaser that was asked in the Singapore and Asian Schools Math Olympiad, and was posted online on 10 April 2015 by Singapore TV presenter. It is an interesting problem and might be asked in the interviews. It is based on logical deduction. It doesn’t require any prior mathematical acumen. It is advised that you try to hustle through the problem yourself without looking at the solution and just to motivate you further to solve the problem, the problem has been talked about in international newspapers like Telegraph and Guardian, so If you are able to solve the problem without looking at the solution you deserve a pat on the back!

**Problem:** It is known that Cheryl’s birthday is one of the following 10 dates listed in the table.

May 15,May 16,May 19,June 17,June 18,July 14, July 16,August 14,August 15,August 17.

May | 15 | 16 | 19 | |||

June | 17 | 18 | ||||

July | 14 | 16 | ||||

August | 14 | 15 | 17 |

Cheryl tells Albert and Bernard separately the month and the day of her birthday respectively.

**Then following conversation takes place**

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

**Bernard:** At first I didn’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?

**Solution:** It is clear that we’ll try to eliminate the 10 choices and finally narrow down to one correct answer based on the arguments given by Albert and Bernard. So let’s eliminate the choices argument by argument.

**Argument 1: ** Albert says, I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know too.

If we look at the dates we observe that if May 18 or June 19 were Cheryl’s birthday then Bernard would have known it instantly because there are only one date with 18 and 19.If Albert knows this fact then he is either told July or August Month. Hence all the dates of May and June are eliminated.

Now the remaining choices are

July | 14 | 16 | ||

August | 14 | 15 | 17 |

**Argument 2:** Bernard says, At first I didn’t know when Cheryl’s birthday is, but I know now.

This eliminates July 14 and August 14 because If Bernard know the exact date, it can’t be 14 as that will create ambiguity between July 14 and August 14.These two dates are eliminated.

The remaining choices are

July | 16 | ||

August | 15 | 17 |

** Argument 3** Albert says, Then I also knows when Cheryl’s birthday is.

If Albert knows the date then it has to be JULY 16 because, in August there are two choices and Albert can’t be sure of his decision. If Albert is absolutely sure then answer is July 16 and all the august dates are eliminated.

**Answer: July 16**

This puzzle is contributed by** Ishaan Arora. ** Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above