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A surprise exam (Posted on 2002-04-26) Difficulty: 3 of 5
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
SolutionProblem SolutionK Sengupta2007-05-28 11:57:59
SolutionStupid Professorjonathan horvat2006-08-10 22:40:39
No SubjectRachael2006-05-18 09:50:11
No Subjectaaron2006-02-14 22:56:18
Some ThoughtsMy opinionFastJazzy2005-11-24 23:04:03
who said it had to be in class?CJ2005-06-17 02:27:22
SolutionNext week.Michael Cottle2004-12-04 04:34:00
solution and possible resolutionlone2004-12-03 07:30:11
Some ThoughtsIf I were the professor . . .Captain Paradox2004-01-04 21:15:35
If this happened to me when i was at school i would have been surprised :)ben2003-12-20 21:36:24
the solution is wrongdonnmike2003-12-03 19:07:23
re: That cannot be.Tristan2003-11-12 19:20:34
That cannot be.Brainteaser2003-11-12 03:34:54
martin gardner's write-upMarc Meyer2003-10-31 12:13:25
On Sunday eveningDacre2003-10-23 11:03:59
re(4): not trueSilverKnight2003-10-07 19:54:00
re(3): not trueGamer2003-10-07 18:16:57
re(2): You guys are forgetting something...Gamer2003-10-01 20:17:07
re: You guys are forgetting something...SilverKnight2003-10-01 18:02:46
Hints/TipsYou guys are forgetting something...Bruno2003-10-01 17:03:26
re: Indirect proofSilverKnight2003-09-30 17:24:52
Indirect proofGamer2003-09-30 17:20:40
re(2): not trueSilverKnight2003-09-30 13:17:49
re: not trueBruno2003-09-30 12:23:22
re: not truesam2003-09-06 15:46:56
not truesrikumar2003-08-29 13:23:04
i must agree to disagreemullen2003-06-21 03:28:59
re: I don't agreeChaz2003-05-03 09:08:45
I don't agreeGamer2003-04-29 12:20:52
No Subjectitduzntmatter2003-04-29 05:26:52
Liar liar!Gamer2003-04-11 13:32:52
Math Classes and SurprisesNigel Nisbet2003-02-14 10:12:44
Amendment 3...just for fun (its short)Greg2003-01-07 22:08:54
Amendment 2?Greg2003-01-07 21:59:04
Solution Amendment?Greg2003-01-07 21:42:49
ParadoxRaveen2002-11-22 03:56:29
FlawJustin Ryan Grenier2002-09-26 07:50:05
Solutionre: SurpriseHappy2002-06-28 12:47:11
SurpriseHalf-Mad2002-05-12 20:57:58
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