Over the years I’ve been in several debates with friends over this problem; it’s a fairly well known math/logic problem:
There’s a class that meets Mon.-Fri. every week, and the teacher announces, “One day next week I will give a pop quiz. You will not know ahead of time what day the quiz will be.”
I claim that this is impossible:
Clearly you can rule out Friday, because if you go through Thursday’s class with no quiz, you’ll know ahead of time it will be Friday.
You can rule out Thursday, since if there’s no quiz through Wednesday, you’ll know ahead of time the quiz is Thursday (Friday’s already out of the picture).
Similarly, Tues. and Wed. can be ruled out, leaving Monday–which can then be ruled out, since now we’ve deduced (before the week even begins) that the quiz will be Monday.
Of course, a 5 day week is just an arbitrary length; the same argument would work for any finite number of days.
So…Do you agree? If so, feel free to respond. If not, where is the error in the logic?
This is a classic one. Martin Gardner covers this in “Gotcha!” By using your logic, you have convinced yourself that the quiz will not happen. And when the teacher hands out the quiz on Tuesday, you will be surprised!
It’s not how you pick your nose, it’s where you put the boogers
If the universe were ruled by straight mathmatical probability, you might be correct. But this is a decision made by a man and not subject to the rules of probability. The Prof. is simply stating that he will not tell YOU the date, he probably already has the day chosen.
Yeah, I don’t think this is realy the case. Once one goes through Thursday’s class, then it can be assumed that the quiz will be on Friday. That is obvious. But that’s where it stops. If one sits through Wednesday’s class then the quiz could be on either Thursday or Friday. It is similar to Xeno’s paradox. Makes sense mathematically, but not spatially.
“And on the eighth day, God Created beer
to prevent the Irish from taking over
the Earth.” ~SNOOGANS~
The problem with this “proof” is that each step relies on the steps after it to be true. A true proof would have each step relying on the steps before it.
Step 1:
“Clearly you can rule out Friday, because if you go through Thursday’s class with no quiz, you’ll know ahead of time it will be Friday.”
This doesn’t work because by step 1 you haven’t determined that you have sat through Thursday without a quiz yet. You have to prove step 2 to prove step 1 and this isn’t how proofs work.
If the above logic was sound you could simply reverse the steps and come up with a vaild proof, but in this case the logic is not sound so you end up with step 1 being “Clearly it could not happen Monday because… well… damn, I guess it could happen Monday!”
I believe the classic version of this is the story of a man who commited a crime so horrible that the judge would not tell him which day of the next week he was to be hung. The judge wanted it to be a surprise.
The convict goes through the same logic as above and is relieved that the judge can’t really surprise-execute him.
And then the punchline:
“On Tuesday morning the convict heard a rattling at his door. He was dragged to the gallows and hung until dead. Boy was he surprised.”
Lots of paradoxes around here lately -Newcomb’s, Hempel’s Raven, and now the Unexpected Examination. I looked this one up in The Paradoxicon, by Nicholas Falletta, which is good reading for those interested in these things. To summarize Falletta’s chapter on this one - the Scottish logician Thomas O’Beirne observed that the paradox arises from the fact that in addition to the two statements:
“There will be an examination” and
“You will not know when it will take place (it will be unexpected)”
there is a third unstated assumption:
“You know these two statements are unconditionally true”
Taken together, the three statements can’t all be true; since the first two are shown to be true after the event takes place, the third must be false.
That’s an interesting way of putting it; it seems to be equivalent to the approach I used–that is, assume the first two statements are unconditionally true (that there IS an exam, and it will be unexpected), arrive at a contradiction, conclude that our assumption of unconditional truth is not valid (the situation is impossible).
