My blog is finally back up after a long hiatus due to hosting problems (not the first time). I’m seriously contemplating moving somewhere more reliable, but it’s hard to come up with a solution that would not (a) invalidate any links to my blog or particular posts, (b) cost a lot of money (my current hosting is free), or (c) require a lot of work to convert/transfer everything. Ideas welcome.
I hope to get back to blogging soon. In the meantime, here’s an old chestnut for you to puzzle over, if you haven’t already seen it:
A certain math class meets every weekday. One Friday at the end of class, the professor tells the class that sometime during the next week, they are going to have a surprise quiz. “I am not going to tell you on what day the quiz will be,” she says. “The only thing I will say for sure is that it will be a surprise—you will not know what day the quiz will be until the moment I hand it out at the beginning of class.”
When will the quiz be?
Feel free to post questions, ideas, and solutions in the comments (so don’t peek at the comments if you want to think about it yourself first).
The Math Less Traveled 
This is supposedly a paradox. The usual thing is to note that it can’t be Friday because then when class finished on Thursday with still no exam, the students would know it must be Friday and so there is no surprise. Since Friday is now excluded, you can apply the same logic to Thursday and so on and conclude that the exam will not be on any day.
After doing that the students feel quite smug and come to school on Monday and before they get a chance to tell the prof that he cannot possibly surprise them, the prof hands out exam papers and the students are indeed surprised!
So the student’s flawless logic has proved there can be no surprise exams and yet there clearly are.
I’ve seen some awfully complicated “resolutions” of this problem but as far as I can tell, there is no paradox, the prof simply said something that isn’t true. If he had said “there’s a 80% chance that you will be surprised” then he would have been correct.
Alternatively, he could defined surprise as “you will not know what day the quiz will be until the last possible moment” and then he would no longer be making untrue statements. So all the way to end of the Thursday class, the student do no know when it will be, they can still be surprised to find out that the exam is in fact on Friday. That’s still within the common definition of “surprise” because maybe it was Friday last time and the prof never does 2 Fridays in a row, so they all crammed for an exam Thursday and were surprised when it didn’t happen.
I’ve seen it said that the paradox is that this proves there can be no surprises but actually what it proves is that if you insist that “surprise” means that
– the participants are told of the existence of the event
– the timing of the event must not be revealed before the event itself
– there are a finite number of times available (say T)
then yes, you cannot guarantee that definition of surprise but if do this over and over, you can still achieve surprise (T-1)/T of the time.
Expect the unexpected and you’ll never be surprised. ;^)
More seriously, professors like this are pains in the ass. Assessment as trickery seems like pretty shoddy pedagogy to me.
Although, if the students know how stupid their professor is for stating a paradox, they know he might give them a quiz on Friday anyway.
I was going to guess Monday, but I have no reasons. Hooray for the blog being back!
always love this one!
more light reading:
http://en.wikipedia.org/wiki/Unexpected_hanging_paradox
Welcome back! (I was starting to think you’d moved to the big blog in the sky).
The “paradox” is equivalent to:
1. There will be a test on one of 5 successive days.
2. It won’t be available on the last available day.
3. It won’t be available on the last available day after applying rule 2.
…
6. It won’t be available on the last available day after applying rule 5.
This isn’t a paradox, it’s just a list of statements, at least one of which must be untrue.
So drop the “beginning of class” and it becomes a lot less interesting.
By the way, I never give surprise quizzes.
Jonathan
Friday
If no test up to Thursday then the assumption is that no “surprise” test can occur on Friday – and similarly thu., wed., tue. mon. The problem is not resolvable unless you accept as this “surprise” as “surprise – your logic is wrong”