Kyle has two friends, Jeff and Shane, who are trying to determine his birthday from a list of ten possible days. Jeff knows the month and concludes that Shane can't know the birthday, leading Shane to determine it after Jeff's statement. Ultimately, both friends deduce that Kyle's birthday is August 25.

1. Kyle has two friends Jeff and Shane. However, they cannot be very good friends because they do
not know Kyle’s birthday! Kyle gives both friends the following ten days and tells them that one
of the given days is his birthday.
May 15
Kyle tells Jeff the month that he was born in, but only the month. Kyle tells Shane the day of his
birthday, but only the day. The following conversation occurs:
Jeff: I don’t know when Kyle’s birthday is, but I know for certain that Shane does not know
either.
Shane: At first I didn’t know Kyle’s birthday, but after what Jeff just said I now know!
Jeff: Well if that is the case then I also know Kyle’s birthday.
When is Kyle’s birthday? Note: You must answer this question by using the given
information.May12
May 15May20June 15June 30July 20July 25July 28August 12August 25
Solution
as jeff know the month and shane know the day
if jeff say that shane does not know either
and shane tell that afeter what jeff just said i know now
so the answer is august 25