**Pigeonhole Principle example question**

a) Show that if five integers are selected from the first eight positive integers, there must be a pair of these integers with a sum equal to 9.

b) Is the conclusion in part (a) true if four integers are selected rather than five?

Solution to this **Discrete Math** practice problem is given in the video below!

**Pigeonhole Principle example problem**

How many numbers must be selected from the set {1,2,3,4,5,6} to guarantee that at least one pair of these numbers add up to 7?

Solution to this **Discrete Math** practice problem is given in the video below!

**Generalized Pigeonhole Principle example**

A drawer contains a dozen brown socks and a dozen black socks, all unmatched. A man takes socks out at random in the dark.

a) How many socks must be he take out to be sure that he has at least two socks of the same color?

b) How many socks must he take out to be sure that he has at least two black socks?

Solution to this **Discrete Math** practice problem is given in the video below!

**Generalized Pigeonhole Principle example question**

What is the minimum number of students, each of whom comes from one of the 50 states, who must be enrolled in a university to guarantee that there are at least 100 who come from the same state?

Solution to this **Discrete Math** practice problem is given in the video below!

**Generalized Pigeonhole Principle example problem**

A company stores public products in a warehouse. Storage bins in this warehouse are specified by their aisle, location in the aisle, and shelf. There are 50 aisles, 85 horizontal locations in each aisle, and 5 shelves throughout the warehouse. What is the least number of products the company can have so that at least two products must be stored in the same bin?

Solution to this **Discrete Math** practice problem is given in the video below!

**Generalized Pigeonhole Principle example #4**

There are 38 different time periods during which classes at a university can be scheduled. If there are 677 different classes, how many different rooms will be needed?

Solution to this **Discrete Math** practice problem is given in the video below!

**RAMSEY THEORY Generalized Pigeonhole Principle example question**

Show that in a group of 10 people (where any two people are either friends or enemies), there are either three mutual friends or four mutual enemies, and there are either three mutual enemies or four mutual friends.

Solution to this **Discrete Math** practice problem is given in the video below!

Thanks so much for providing individuals with an extremely helpful tutorial on pigeonhole principle.

Please post more of these, so much fun to practice them!

Wonderful and helpful examples, thank you