perplexus.info :: Paradoxes : A surprise exam

A surprise exam (Posted on 2002-04-26)

A professor tells his class that he will give them a surprise examination sometime next week.

For our purposes, an examination is considered a "surprise" if on that day, the class is not 100% sure that they will get an examination. (If they only suspect it, the examination can still be a surprise.)

Having given the class this warning, is it still possible for the professor to give them a surprise examination next week? (Assume that he will not give them an exam if it will not be a surprise.)

Submitted by levik

Rating: 3.3684 (19 votes)

Solution: (Hide)

The paradox here is in the reasoning that the professor cannot "surprise" his class with an exam on friday - since they know that they will get an exam this week, and didn't get one in the first four days of the week, they will know that friday must be the day, and so it is no longer a surprise.
But then by the same logic, since now the exam can only be given on Mon - Thu, giving it on Thursday, the last possible day, would not be a "surprise" either.
This way, we can eliminate all the other days of the week one by one, and by this logic, the professor cannot give the students a surprise exam.
However as soon as the class knows that the professor cannot give them a surprise exam during the week, the exam can be given on any of the days and be a surprise (since the class doesn't expect it).

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Problem Solution	K Sengupta	2007-05-28 11:57:59
Stupid Professor	jonathan horvat	2006-08-10 22:40:39
No Subject	Rachael	2006-05-18 09:50:11
No Subject	aaron	2006-02-14 22:56:18
My opinion	FastJazzy	2005-11-24 23:04:03
who said it had to be in class?	CJ	2005-06-17 02:27:22
Next week.	Michael Cottle	2004-12-04 04:34:00
solution and possible resolution	lone	2004-12-03 07:30:11
If I were the professor . . .	Captain Paradox	2004-01-04 21:15:35
If this happened to me when i was at school i would have been surprised :)	ben	2003-12-20 21:36:24
the solution is wrong	donnmike	2003-12-03 19:07:23
re: That cannot be.	Tristan	2003-11-12 19:20:34
That cannot be.	Brainteaser	2003-11-12 03:34:54
martin gardner's write-up	Marc Meyer	2003-10-31 12:13:25
On Sunday evening	Dacre	2003-10-23 11:03:59
re(4): not true	SilverKnight	2003-10-07 19:54:00
re(3): not true	Gamer	2003-10-07 18:16:57
re(2): You guys are forgetting something...	Gamer	2003-10-01 20:17:07
re: You guys are forgetting something...	SilverKnight	2003-10-01 18:02:46
You guys are forgetting something...	Bruno	2003-10-01 17:03:26
re: Indirect proof	SilverKnight	2003-09-30 17:24:52
Indirect proof	Gamer	2003-09-30 17:20:40
re(2): not true	SilverKnight	2003-09-30 13:17:49
re: not true	Bruno	2003-09-30 12:23:22
re: not true	sam	2003-09-06 15:46:56
not true	srikumar	2003-08-29 13:23:04
i must agree to disagree	mullen	2003-06-21 03:28:59
re: I don't agree	Chaz	2003-05-03 09:08:45
I don't agree	Gamer	2003-04-29 12:20:52
No Subject	itduzntmatter	2003-04-29 05:26:52
Liar liar!	Gamer	2003-04-11 13:32:52
Math Classes and Surprises	Nigel Nisbet	2003-02-14 10:12:44
Amendment 3...just for fun (its short)	Greg	2003-01-07 22:08:54
Amendment 2?	Greg	2003-01-07 21:59:04
Solution Amendment?	Greg	2003-01-07 21:42:49
Paradox	Raveen	2002-11-22 03:56:29
Flaw	Justin Ryan Grenier	2002-09-26 07:50:05
re: Surprise	Happy	2002-06-28 12:47:11
Surprise	Half-Mad	2002-05-12 20:57:58

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