Brain Treaser

[vk6ti]

Some one challenged me with this brain teaser, I got half way through it and impatiently conceded defeat, It is out there on the web, and there is an answer.
I thought some of you out there may enjoy it.
I hope the image comes through
Ray

   

[Marcus von Cube]

Thanks for the nice riddle! Let me try:

A knows the month (one of May, June, July, August). He cannot know the exact date but he knows that B can't either. This rules out May and June because if it were one of the latter there is the possibility that B were told days 18 or 19 which are unambiguous. Therefore we have either July or August.

Now, B knows the exact date. He does the same reasoning as above and rules out May and June. He states that he now has enough information to know the exact date. So the day cannot be 14 which is ambiguous, so it must be one of 15, 16 or 17.

Now A knows that B knows the exact date. If the month were August, A still would have two choices, August 15 or August 17, but he states that he now knows the date, too. This leaves only July 16 as the solution.

[Tugdual]

Thanks Marcus.
All the sudden I realize why other forums have a "[spoiler]" tag ;-).

[vk6ti]

Marcus
Sehr gut
Well done,I got to the 18 and 19th reasoning, but then I had to look answer up as I don't have the patience, or time, so in this instance I "cheated". I now wish I dedicated the time to keep at it as I spent more time on the answer than I did the question
Just as well it's only a bit of fun
Ray