The Unexpected Examination

On friday afternoon in class, the Headmaster tells his students that next week, they are to have an unexpected exam. That is, there will be an exam but they don't know on which day it will occur.

Over the weekend, the students gather and using logic, try to determine which day the exam will be.
"If thursday afternoon comes, and there has been no exam, then we can be sure that the exam is on Friday. Therefore, the Headmaster can't put the exam on friday. Likewise, on Wednesday afternoon, if there is no exam, we will know it will be on Thursday. Therefore, the exam can't be on Thursday." The students follow this line of logic to Monday.

Having 'proved' that the exam can't exist, the unexpecting students are given the exam on Tuesday morning.

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This is a philosophical problem I heard recently. Superficially, the students' logic seems great. However, they are still given the exam. Does the hole in their logic lie in linguistics (i.e. of the word 'unexpected')? Does it lie in the fact that they pile their proofs on top of each other (i.e. trusting that the exam can't be on friday, thursday, wednesday AND tuesday, and therefore not monday)?

The problem is in the linguistics.

As soon as the teacher tells the students that they have an exam next week, it's no longer unexpected.

Also the teacher says you will have an unexpected exam... Like BB said now they know they will have an exam so it is not unexpected. What the teacher means at this moment you don't know when the exam will be. To say it cannot be on friday because on thursday they would know it would have to be on friday is not logic... (at the moment they are told they will have the exam)