Unexpected Exam Paradox – Webtekno

One of the scariest sentences of our school years “Take out the papers, I’m taking an exam.” it could be. You have no preparation, you are close to failing in mathematics… There is also a less scary version of this saying. “Next week I will never see you again. when you least expect it “I will take an exam.”

This sentence is slightly better than the sudden exam because you have time to study. So can you guess which day the exam will be? If you’re ready, you’ll see all this chaos. By combining them in the “surprise exam paradox” Let’s clear our minds thoroughly.

Let’s take a journey back to your high school years.

Let’s say your last class on Friday is math (worse than a nightmare). There are five minutes until the bell, your mind is spinning, and you are happily preparing your bag. Attends your classes five days a week Your teacher suddenly says the following sentence: “I will give you an exam next week on a day you least expect. Study well on the weekend as you never know what day it is!”

The teacher says this sentence and leaves the class. And you’re left feeling demoralized and confused. Well, guessing with your friends Which day will the exam take place? can you find it?

The following dialogue may occur between you and your friends:

A: “It is impossible to have the exam on Friday because at the end of the lesson on Thursday, we could understand that the exam will be held on Friday.”

B: “If it cannot be held on Friday and the exam has not been completed by Thursday, we also understand that the exam will be held on Thursday. “Then not on Thursday, but before.”

A: “Then, with a similar logic, we can eliminate Wednesdays, Tuesdays and Mondays.”

D: “Why did we eliminate Monday?”

TO: “If Monday is the only possible day, then there will be no surprises on that day either.”

F: “Well then, it is impossible to take this exam. “Let’s go to the PS cafe and play games.”

What happens when the expected week arrives?

Concluding that a surprise exam was impossible, students did not study at all on the weekend. But their teachers He takes an exam on Wednesday! Of course, whatever happens… The students’ predictions about the impossibility of the exam did not come true.

It is impossible for the exam to be impossible.

If we consider the same method of reasoning from a later date, it turns out to be wrong. We can explain it like this: If the teacher had told the students at the beginning of the semester that he would have an unexpected exam during the semester, he would have used the same reasoning. We would reach the conclusion that the exam could not be held again. But it is a fact that there will be at least one exam during the semester.

Another reason is that reasoning self-deception Because students are surprised when there is an exam any day. Whether it’s Tuesday or Wednesday. The teacher said, “Prepare your paper and pencils. “I will take an exam.” From the moment he says it, it becomes a test with all kinds of surprises.

This “unexpected/surprise exam paradox”; It has been making logicians, mathematicians and philosophers think for many years, but they still have not managed to overcome the paradox. We are looking forward to your thoughts in the comments!

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