This is the second part of the solution for the problem which I provided a couple of days ago. If you have not read this then please start from the first part of this problem – When is Cheryl’s birthday.

Yesterday I provided the first hint to you, and we concluded with the following:

STATEMENT 2: Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.

The question to ask is: how does Albert KNOW that Bernard does NOT KNOW the birthday!

We can also ask this another way – HOW could Bernard KNOW the birthday, and how would Albert also KNOW that Bernard KNOWS?

This is actually more simple that it looks.

Since there is only one date for each of the days 18 and 19, if Bernard was told by Cheryl that it was one of these two days (remembering that Cheryl told Bernard ONLY the day of her birthday and not the month), then this would be simple.

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

By Albert does not know what the day it, but DOES KNOW that Bernard does NOT KNOW. If Albert (who was told only the month of the birthday), was told that this was May or June, then we would know that Bernard MAY KNOW the correct birthday if it was 18 or 19. However, if it was not May or June, then there are always at least two options, and so Bernard CANNOT KNOW exactly which is the correct date.

This we can conclude that Albert was told that the month was either July or August, and that Bernard was told a day other than 18 or 19.

So now we come to the next statement:

STATEMENT 3: Bernard: At first I don’t know when Cheryl’s birthday is, but I know now.

Bernard is able to tell which is the correct date simple from what Albert said in STATEMENT 1. So how could he deduce this?

This will be concluded in the final installment of this set of posts.

You should work this out yourself, and you will need to use the final statement as well.

STATEMENT 4: Albert: Then I also know when Cheryl’s birthday is.

See tomorrow for the final part of the solution of this interesting problem.