May 1, 2025
Science

The ‘coin-flip paradox’ that makes you do somersaults in an attempt to find the answer

  • December 22, 2023
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In fact, we encounter this paradox every day, we just aren’t aware of it. Apparently practiced in America Scholastic Aptitude Test This was also overlooked in the (SAT)

In fact, we encounter this paradox every day, we just aren’t aware of it. Apparently practiced in America Scholastic Aptitude Test This was also overlooked in the (SAT) exam. Because when a question was asked about this paradox, even those who prepared the question gave the wrong answer!

If you want to flip a coin on the table, it seems very normal; but as the money spins, it suddenly seems like it’s spinning at two different speeds. In this situation we haveCoinFlip paradox‘ we say. Let’s go into detail and see if you also give the wrong answer.

This paradox is addressed in the SAT exam for college admissions in America.

This exam is an international exam valid for US citizens and foreign students. Candidates; They are assessed in writing, verbally and mathematically.They are subjected to an exam with multiple choice questions.

A math question on this exam in 1982 It has officially gone down in history. This question was so difficult that no student could find the correct answer. Even those who prepared the question could not fully solve the question.

It seems like people are wondering this question. Let’s show it now:

In the figure, the radius of circle A is the radius of circle B. It’s 1/3 of it. From the position shown in the figure, circle A rotates around circle B. it starts rolling and then returns to the starting point. For this How many revolutions must circle A make in total?

As with any exam, speed is also important for this exam.

The answer to this question is up to you It may have looked like 3; As a result, if we assume that the radius of circle B is three times the radius of circle A, the circumference of B will be three times the circumference of A.

The process of opening the small circle and wrapping it around the larger circle would occur exactly 3 times. If you look at it that way Even though the answer seems to be 3 Unfortunately, you’ve been eliminated too!

The interesting thing is that all other options were wrong. The correct answer was 4 And that wasn’t even an option.

This interesting incident later “currency rotation paradox” It started to be mentioned. Because the result of the problem expressed a paradoxical situation because it seemed counterintuitive. We see again how important small details can be in such exams.

If we simplify the question a bit…

Place two coins of the same size on the table. When the left coin is rotated in the direction of the arrow around the center coin Does it turn a full turn or half a turn? If you are too lazy to try, the answer is one full tour. So the money is intended to go back to where it started two full turns He must have thrown it.

If we accept the radius of the coin as r, the distance the center of the coin travels is the same 1/2×2πx2r=2πr It will happen. In this case, the coin must rotate around itself twice to complete one rotation around the center of the coin.

In the case of two circles rotating around each other, you need to proportion the circumferences of the circles and add 1 to the result to find the number of revolutions of the moving circle. This is where the SAT question error came from.

In this case, when the right coin is rotated around the center coin, the center coin only makes one full rotation around itself. In other words, the coin rotated clockwise makes only one revolution around itself to return to its starting point. This is the result of the calculations made and solves the paradox.

Sources: Medium, Scientific American

For other math problems:

Source: Web Tekno

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