How Many Humans Have the Same Number of Body Hairs?

The video explores whether two people in the world have the same number of body hairs, using the pigeonhole principle to demonstrate that it's guaranteed. It explains the principle with historical and modern examples, showing its application in various scenarios. The video also introduces an advanced version of the principle, illustrating its use in complex mathematical problems.

Why is it guaranteed that two people in the world have the same number of body hairs?

• Because there are more people than possible hair counts.

• Because everyone has the same number of hairs.

• Because hair counting is inaccurate.

• Because body hair doesn't vary much.

What is the pigeonhole principle?

• A method to count pigeons.

• A principle stating that if you have more items than containers, some containers must hold multiple items.

• A way to organize data efficiently.

• A principle about the distribution of birds.

Which historical publication discussed the pigeonhole principle?

• The Athenian Mercury

• The New York Times

• The Scientific American

• The British Gazette

How does the pigeonhole principle apply to PIN numbers in a college?

• All students have unique PINs.

• At least two students share the same PIN.

• PINs are assigned randomly.

• PINs are not used in colleges.

What is a practical example of the pigeonhole principle in an elevator?

• Some buttons are pressed multiple times.

• All buttons are pressed by one person.

• Each person presses a unique button.

• No buttons are pressed.

What does the advanced version of the pigeonhole principle state?

• It only applies to birds.

• It divides items equally among categories.

• It ensures at least N/K items in some category.

• It is not applicable to real-world scenarios.

How many people are estimated to have the same number of body hairs according to the advanced pigeonhole principle?

• At least 19 people

• At least 50 people

• At least 10 people

• At least 5 people