"The Impossible Exam"

[iago]

This is an interesting problem one of my professors proposed to us yesterday that I can't, for the life of me, figure out a solution to.  Clearly, there must be a logical fallacy somewhere in it, because the answer makes no sense, but I can't figure out what it is.

Anyway, here it is:
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The setup:
Let's say that one of your professors wants to give you a surprise test next week, on either Monday, Tuesday, Wednesday, Thursday, or Friday (I'll abbreviate it MTWRF because I'm lazy).  The problem is, he wants it to be a secret, so if somebody finds out somehow that the test is happening on that particular day, he'll cancel it and give everybody full marks.  We're assuming that there's only necessarely one person who has to guess for the purpose of this (for a more realistic problem, say there's 120 possible days or something).

The problem:
First of all, if we get to friday then we can be totally sure that, if we haven't had the test yet, it has to occur on that day, and we can guess it, so we can safely assume it's not going to happen on friday, leaving us with only 4 possibilities: MTWR.

Now, if he gives it to us thursday, because it's impossible on friday, we'll know and guess it, leaving us with only 3 possibilities, MTW.

If it's wednesday, we'll know: MT

If it's tuesday, we'll know: M

If it's monday, we'll know: [null]

Therefore, it's impossible to give that type of a test, because there aren't any possible days.
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There's another problem similar to that he also posed to us, but it's a lot less realistic, and takes longer to explain, so I might post it later.

[Grok]

Nah, Friday's not eliminated until Thursday.

So on Wednesday, you still don't know whether the test is today or tomorrow.  Making Wednesday a completely viable option.

[iago]

Yeah, I think you're right.. as I was typing it, I got the same idea, that the next day can't be elimated until the day before it is.

However, you still have the option to make plans to go out and get wasted on thursday night anytime during the week, because even if the exam is on friday, all you have to do is show up (hung over) and declare that you know it's today.  That's what my prof said, anyway, and he says he wants to try this some year to see what happens

[Adron]

All you have to do is change your guess every day. On monday you guess monday, on tuesday you guess tuesday and so on. If you're not forced to pick a particular single day for your guess, then yes, it is impossible.