The teacher announced that there will be a surprise test next week.

The class meets on Monday, Wednesday, and Friday. If the test is given on Friday, then on Thursday I would be able to predict that the test is on Friday. It would not be a surprise.

Can the test be given on Wednesday? No, because on Tuesday I would know that the test will not be on Friday (thanks to the previous reasoning) and know that the test was not on Monday (thanks to memory). Therefore, on Tuesday I could foresee that the test will be on Wednesday. A test on Wednesday would not be a surprise.

Could the surprise test be on Monday? On Sunday, the previous two eliminations would be available to me. Consequently, I would know that the test must be on Monday. So a Monday test would also fail to be a surprise. Therefore, it is impossible for there to be a surprise test.

Can the teacher give a surprise test?

[Edited on February 24, 2010 at 1:32 PM. Reason : ]

2/24/2010 1:31:40 PM

wtf you wouldn't be able to make both of the first eliminations on sunday

the second hinges entirely on you having gone to class and not having had a test monday

2/24/2010 2:49:37 PM

If you know there's going to be a test, it's not a surprise.

2/24/2010 2:54:04 PM

How can a test be a surprise if you are forewarned about it? The day it occurs on could be a surprise as you will be surprised Monday and Wednesday if the teacher decides to wait until Friday.

In other words, if you expect something to happen every single day, then how is going to surprise you? What you expect doesn't happen, that's how.

2/24/2010 2:54:55 PM

But it's so simple. All I have to do is divine from what I know of you: are you the sort of man who would put the quiz on Friday or Monday? Now, a clever man would put the quiz on Friday, because he would know that only a great fool would expect a quiz on Friday. I am not a great fool, so I can clearly not study for the quiz on Friday. But you must have known I was not a great fool, you would have counted on it, so I can clearly not study for the quiz on Monday.

2/24/2010 2:55:18 PM

I forgot what undergrad class I first heard this reductio ad absurdum paradox before, it was definitely as CSC class though. Obviously, if you could move backward through time this question would be a paradox, but if we're allowing backward time travel this paradox is the least of our concerns.

Also:
http://xkcd.com/246/

2/24/2010 4:49:00 PM

shut the fuck up

2/24/2010 4:51:29 PM

You only think I guessed wrong! That's what's so funny! I switched test dates when your back was turned! Ha ha! You fool! You fell victim to one of the classic blunders - The most famous of which is "never get involved in a land war in Asia" - but only slightly less well-known is this: "Never go against a Sicilian when test grades are on the line"! Ha ha ha ha ha ha ha! Ha ha ha ha ha ha ha! Ha ha ha--

2/24/2010 7:16:31 PM

How has zero people gotten this yet?

2/24/2010 7:36:38 PM

I don't think that's the case.

It's just not as clever as he thinks it is.

2/24/2010 9:34:43 PM

I think we have all seen "The Princess Bride" before, but I have heard this posed elsewhere before.

Oh, now I remember... We talked about this in an e-commerce class when discussing the auction concept of "cheap talk". I think he even showed the clip from this part of the movie. I suppose that makes this an unintentional excellent parody.

2/24/2010 11:30:35 PM

^I think most people know it as the more famous example: the hangman paradox. A judge sentences a man to be hanged next week, the day will be a surprise. The prisoner reasons that he will not be hanged next week because it will not be a surprise following the same logic in the OP.

2/25/2010 12:51:05 PM

^thats what I was thinking too.

It was worded a little funky the first time I read it in the OP, but I guess it gets the point across.

From wikipedia (for people who haven't heard of this "paradox" before):

Quote :

"A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day. Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts. He begins by concluding that the "surprise hanging" can't be on a Friday, as if he hasn't been hanged by Thursday, there is only one day left - and so it won't be a surprise if he's hanged on a Friday. Since the judge's sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday. He then reasons that the surprise hanging cannot be on Thursday either, because Friday has already been eliminated and if he hasn't been hanged by Wednesday night, the hanging must occur on Thursday, making a Thursday hanging not a surprise either. By similar reasoning he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all. The next week, the executioner knocks on the prisoner's door at noon on Wednesday — which, despite all the above, will still be an utter surprise to him. Everything the judge said has come true."

[Edited on February 25, 2010 at 1:02 PM. Reason : ]

2/25/2010 1:02:11 PM

I've just decided to switch our Friday schedule to Monday, which means that the test we take each Friday, on what we learned during the week, will now take place on Monday, before we've learned it. But, since today is Tuesday, it doesn't matter in the slightest.

3/3/2010 1:42:09 AM

(Today is Wednesday.)

3/3/2010 9:20:31 AM

^its another movie quote

3/3/2010 12:57:01 PM

Quote :

"I don't think that's the case. It's just not as clever as he thinks it is."

4/6/2010 12:09:23 PM