Quoted By:
>Ash: I don't know when Cheryl's birthday is, but I know that Brock doesn't know too.
Ash could never know when Cheryl's birthday is given only the month, this first clause is irrelevant. However, the second half of Ash's statement implies that the month is not May or June: otherwise, for all Ash knows the birthday could be May 19 or June 18, in which case Brock would know the full birthday from just the day. So, Cheryl's birthday must be in July or August.
>Brock: At first I don't know when Cheryl's birthday is, but I know now.
This tells us that Cheryl's birthday does not fall on the 14th. Otherwise, Ash eliminating May and June would not have helped Brock to determine the full birthday. So, Cheryl's birthday falls on either July 16th, August 15th, or August 17th.
>Ash: Then I also know when Cheryl's birthday is.
If Ash was told August, he could not know when Cheryl's birthday is at this point, because he would still have two options between the 15th and 17th. So, he must have been told July, leaving only July 16th.
QED. Now if only I could solve the Captcha.
