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Surprise Examination Problem

This puzzle puzzles me the most. It is a very famous one and many of you might have already encountered it.

Consider a professor telling his class: ?There will be a surprise exam during class next week?.There are 5 days in a week, class meets every day. Can the professor give a surprise exam? As usual, the professor and the students are very intelligent.

Surprise is defined as: Student does not know at the beginning of class that the exam is during that class.


vivek gupta
Saturday, April 20, 2002

so I guess the logic goes: he can't give a surprise test on friday, because if there's no test by then, the students will know it's on friday. Also, by the same token, thursday is no good, etc.

But why not just pick a random day mon - thur and give it then? what would be unsurprising about that?

Saturday, April 20, 2002

That exactly is the paradox. There seems to be no flaw in the argument for his being not able to give the exam.
But we all know that he can easily give a surprise exam.

vivek gupta
Saturday, April 20, 2002

Speaking from experience, if a prof. promised a surprize test "next week" and gave it on monday of that week, I would be very surprised :)

Saturday, April 20, 2002

Can the professor say on Monday that the test will occur on Wednesday and then actually give the test on Tuesday?

Can the professor offer the "surprise" test on Monday - and then give a real surprise test on Tuesday?

Friday, May 17, 2002

It's a backwards reasoning fallacy, assuming that the students know on *Thursday* that the test is going to be on Friday.  Let's go through it:

On Friday, the students know the test must be on that day; they have the information about a test that week combined with the lack of a test on the four previous days.

On Thursday, the students know the test must be on either Thursday or Friday.  Therefore, a test will surprise them.

Perhaps the problem is that the word "surprise" implies 0% expectation of an event?

Jason McCullough
Thursday, May 23, 2002

This can be done.Say the professor didn't conduct the exam in the first four days.So now it's friday and students are sure that there won't be any exam today since the professor can't surprise them.Now if he conducts the exam ,the students will be surprised. 

vimal Earnest
Friday, May 31, 2002

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