Something to Ruin Your Weekend
| Lasse Lien |
On a Monday morning, a professor says to his class, “I will give you a surprise examination someday this week. It may be today, tomorrow, Wednesday, Thursday, or Friday at the latest. On the morning of the examination, when you come to class, you will not know that this is the day of the examination.”
Well, a logic student reasoned as follows: “Obviously I can’t get the exam on the last day, Friday, because if I haven’t gotten the exam by the end of Thursday’s class, then on Friday morning I’ll know that this is the day, and the exam won’t be a surprise. This rules out Friday, so I now know that Thursday is the last possible day. And, if I don’t get the exam by the end of Wednesday, then I’ll know on Thursday morning that this must be the day (because I have already ruled out Friday), hence it won’t be a surprise. So Thursday is also ruled out.”
The student then ruled out Wednesday by the same argument, then Tuesday, and finally Monday, the day on which the professor was speaking. He concluded: “Therefore I cannot get the exam at all; the professor cannot possibly fulfill his statement.” Just then, the professor said: “Now I will give you your exam.” The student was most surprised, but the professor seems to have kept his word.