Alky wrote: ... First of all, "know when the test is" is clearly dependent on time.
Alky wrote:The problem should probably be rephrased so the students must say "the test is today" at the beginning of the day (and the professor can't just change his mind!).
Alky wrote:However, rereading the story it looks like it is stated in such a way to cause the "multiple guesses when you're wrong" scenario.
Alky wrote:I would bet this is just an example of a contradiction via self reference (the students are considering their own actions based on their considerations of their own actions). In fact, if you do a 'formal' proof of the situation, you get a contradiction (which allows you to then state 'the test is on Wednesday').
notzeb wrote:This one's easy! The professor's lying.
...Or he would be lying, if any of the students were smart enough to realize it. Basically, they stupidly believed his lies, and by believing them, they made them true.
Edit: Imagine I told you you'd have a surprise exam tomorrow, and that you wouldn't expect it. It's pretty much the same thing.
Patashu wrote:On Tuesday, if the exam has not happened it is actually more likely for it to be on wednesday, now that there's a hint of ambiguity (both wednesday and thursday could reasonably hold it).
bbctol wrote:Well, if the exam is a surprise, that just means it happens on a day when they expect it not to. And they don't expect it on any day. So it's a surprise on any day. Right?
Actually, I still think it can't be friday, and I don't like my own logic. Wah.
Your answer is fundamentally irrational, though I don't blame you for not noticing it.silverhammermba wrote:I've always kind of hated this question and mainly because of the ambiguity of "knowing which day the exam is on". That phrase can be written any number of subtly different ways. And I agree with jordan that it's a contradiction.
There's also a critical flaw in the student's reasoning
Think about it:
1. Exam will be given some day Monday-Friday
2. If, come Thursday, the exam has not been given, the students will know it is Friday. So the exam must be given Monday-Thursday
3. Come Wednesday, the student does not yet know if the exam will be given on Thursday or not and thus cannot rule out Friday as well.
4. Thus the exam can be given on any day Monday-Thursday and will be a complete surprise
The key is that information is revealed chronologically.
Basically: you can only rule out Friday once you know that the exam is not given on Thursday.
I present the conjecture: there is no way to determine whether or not the exam will be given on Thursday ahead of time.
I'm very certain in my answer.
You can. It just... doesn't look like a cake anymore.Do you see what I'm getting at? You can't have a cake that you've eaten.
There will be an exam on Friday.
You will be surprised by the exam on Friday: there is no way to prove that the exam is on Friday.
Suppose the professor wrote:There will be an exam one day next week. Each day next week, you will not be sure whether the exam will be that day.
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