Member: Rank 8
A reliable teacher announces there will be a surprise exam one weekday of the following week. The pupils reason that it can't be Friday, since if it hasn't come by Thursday evening they will expect it the following day, and then it won't be unexpected. If it hasn't come by Wednesday evening they will rule out Friday for the reason just given, but then it won't be a surprise on Thursday, and so that day is ruled out too. And so backwards through the week. So the teacher's announcement cannot be fulfilled. But surely there can be a surprise exam. What is wrong with this seemingly logical reasoning?