OK, how is this:
RogerS wrote:I know how you chaps like a challenge.
The teenage maths test
Albert and Bernard want to know when Cheryl’s birthday is. Cheryl gives them ten possible dates:
May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15, August 17
Cheryl then tells Albert the month in which her birthday falls, and she tells Bernard the day’s number.
Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.
If Albert knows that Bernard doesn't know, then it cannot be on a date that is only present in 1 month. Thus it cannot be May 19 or June 18, since if Bernard was given the numbers 18 or 19 he would know which of the 10 possible dates it had to be. If it cannot be those dates and Albert still doesn't know which day is Cheryl's birthday, then it must be in a month that has two possible choices left. As a consequence it cannot be June 17th.
Bernard: At first I didn’t know when Cheryl’s birthday is, but I know now.
We are currently left with 7 possible dates. If Bernard (who is given the date, not the day) now knows when it is, only 1 of the 7 dates is unique - there are two 14's, two 15's, two 16's and one 17. Thus Bernard must have been given the number 17 to know when Cheryl's birthday is.
Albert: Then I also know when Cheryl’s birthday is.
If Albert has eliminated June 17th already ,and Bernard now knows, then Cheryl's Birthday must be August 17th.
Don't know if this is right, but it seems logical......
Steve