# Solution to “When is Cheryl’s Birthday?” – Math Problem

Come let’s figure out when Cheryl’s birthday exactly is.

So here is the question:

The first clue from Albert is: I don’t know when Cheryl’s birthday is, but I know Bernard does not know, too.

How can Albert be so sure? Bernard would have known the answer only if the date he knows is 18 or 19. Since these are the only two dates which appear once. Hence May and June options are ruled out. (Albert wouldn’t have made the above statement if the month he got was May or June)

Following this statement Bernard knows that May and June are ruled out. And then he says: At first I didn’t know, but now I know.

Eliminating May and June, five possibilities are left:

July 14      July 16

August 14     August 15    August 17

If the date Bernard knew was 14, he would not have made above statement as he would be having two possibilities(July 14 and August 14). So these two options are also eliminated.

Hence we are left with three options July 16August 15 and August 17.

Now Albert says: Well, now I know too!

Since Albert only knew the month, he can only be sure if it is July. (Because August would again give two possibilities)

So from above three options now we also know that Cheryl’s birthday is on 16th July. 🙂

Finally I would like to have a word with Cheryl: “Hey Cheryl! What kind of a person your are? You could have just told the exact date instead of playing all these games and saved us with all this trouble.

Let me know if you got the solution straight. Else good luck scratching your head!!! 🙂 🙂

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