At the end of class on a Friday afternoon, a math teacher announces the following to
his students:
"I will be giving a pop quiz some day next week, and I guarantee you will not know
the quiz is happening until you come into class that day."
Gina, one of the students in the class, thinks about the teacher's statement and determines that the quiz could not possibly be on Friday, because if it were, then
all of the students would know this on Thursday night, which would would contradict what the teacher said about the quiz being a surprise.
She then determines the quiz could not be on Thursday either, because if it was,
all the students would know by Wednesday night (since the quiz hadn't yet happened,
and thus must be on Thursday or Friday, but since we already determined it couldn't
be on Friday, it must be Thursday). Again, this wouldn't be a surprise, contradiciting
what the teacher said, and so the quiz couldn't be on Thursday.
Using the same logic, she then determines that the quiz could not be on Wednesday,
or Tuesday, or Monday. Thinking that the teacher must have been contradicting
himself, Gina decides the quiz couldn't be any day of the week, and decides to not
bother studying for it.
Much to Gina's surprise, the teacher announces on Tuesday that he is giving a pop
quiz. Gina is surprised, just as the teacher said she would be.
What was wrong with Gina's reasoning?
