Why surprise exams are impossible.
A teacher announces to his class that he will hold a “surprise” exam on exactly one of the five days (Monday to Friday) of the next school week. The exam will be a “surprise” (the teacher goes on to explicate) in the sense that the students will not know the day of the exam until that day arrives.
Most of the students sigh and resign themselves to a weekend of studying. But one clever student argues instead that what the teacher says is impossible. “No such surprise exam can take place!”, he exclaims, offering the following reasons:
“Clearly, the exam cannot be held on Friday (the last day of the school week), because, if it were held on Friday, then we would know about this by the end of Thursday, seeing that no exam had yet been held, and only one day was left. But the teacher said that we would not know the day of the exam until that day itself. This shows that the exam cannot take place on Friday.
“But in that case, the exam cannot be held on Thursday either! For if it were held on Thursday, then we would know about this by the end of Wednesday, seeing that no exam had yet been held and only two days (Thursday and Friday) were left, but we have already ruled out Friday! But the teacher said that we would not know the day of the exam until that day itself. This shows that the exam will not take place on Thursday either.
“The exam cannot be held on Wednesday either, because by the end of Tuesday we will know that the exam must be on Wednesday, Thursday or Friday; but having already eliminated Thursday and Friday, the exam must be on Wednesday. The exam therefore cannot be on Wednesday.
“Tuesday seems the most promising and probable day, but in truth it is also impossible to hold the exam on Tuesday, as by Monday evening we will have safely dismissed the possibility that it will be on Wednesday, Thursday and Friday; leading us to conclude on Sunday night that Monday must be the exam, from which conclusion we therefore infer that the exam cannot be on Monday.
“As you can see, it is not allowable by the laws of the logical universe to have a surprise exam next week. Quod erat demonstratum”
Most of the students sigh and resign themselves to a weekend of studying. But one clever student argues instead that what the teacher says is impossible. “No such surprise exam can take place!”, he exclaims, offering the following reasons:
“Clearly, the exam cannot be held on Friday (the last day of the school week), because, if it were held on Friday, then we would know about this by the end of Thursday, seeing that no exam had yet been held, and only one day was left. But the teacher said that we would not know the day of the exam until that day itself. This shows that the exam cannot take place on Friday.
“But in that case, the exam cannot be held on Thursday either! For if it were held on Thursday, then we would know about this by the end of Wednesday, seeing that no exam had yet been held and only two days (Thursday and Friday) were left, but we have already ruled out Friday! But the teacher said that we would not know the day of the exam until that day itself. This shows that the exam will not take place on Thursday either.
“The exam cannot be held on Wednesday either, because by the end of Tuesday we will know that the exam must be on Wednesday, Thursday or Friday; but having already eliminated Thursday and Friday, the exam must be on Wednesday. The exam therefore cannot be on Wednesday.
“Tuesday seems the most promising and probable day, but in truth it is also impossible to hold the exam on Tuesday, as by Monday evening we will have safely dismissed the possibility that it will be on Wednesday, Thursday and Friday; leading us to conclude on Sunday night that Monday must be the exam, from which conclusion we therefore infer that the exam cannot be on Monday.
“As you can see, it is not allowable by the laws of the logical universe to have a surprise exam next week. Quod erat demonstratum”
posted by cp at
12:57 AM
0 Comments:
Post a Comment
<< Home