Pigeon-Hole Principle By: Olivia Nielsen, Jordan Reid,

Allison Mckenzie, Paige Brelser

Why was this video created?

• This video was created as a technology requirement for our Math 551 class at Central Michigan University.

What is the Pigeon-Hole Principle?

• The Pigeon-Hole Principle states that if p items (Pigeons) are put into h pigeonholes with p>h, then at least one pigeonhole must contain more than one item.

This pigeonhole contains more than one pigeon.

Example Problem

There are 3 pigeonholes and 4 pigeons

Example Problem

We can evenly distribute a pigeon into each of the pigeonholes, leaving one pigeon leftover.

Example Problem

The result is that at least one hole has two pigeons because the number of pigeons is greater than the number of holes. P>H

Try it on your own!

• There are 25 students in the class. Each student received an A, a B, or a C on their math test. Show that there are at least nine students who received the same grade on the test.

Here’s a Hint!

• The students are the pigeons and the grades are the holes!

A B C

Here is how we se up the problem. We have 3 holes, for the grades, and 25 students.

A B C

We can evenly distribute the students into each of the holes. One student is remaining.

A B C

We can show that nine students have the same grade because the number of students is greater than the number of holes.

Problem Overview

• Since 25 = 3 x 8 + 1, we were able to equally distribute the students into the letter grades. With eight students in each letter grade, there was one student leftover. Therefore, one of the grades must have nine students with the same letter grade.

Summary

• Why would teachers use the pigeon-hole principle to teach students?– Differentiation for grade levels– Provides a visual to learn mathematical

concepts– Improves problem solving skills

We hope you are one of thosenine students who will receivean A on your next math test!!!

Credits

• Producer: Olivia Nielsen• Writers: Olivia Nielsen, Jordan Reid, Allison

Mckenzie, Paige Brelser• Narrators: Olivia Nielsen, Jordan Reid,

Allison Mckenzie, Paige Brelser• Reference:

– "Problems with a Point." The Pigeon-Hole Principle Problem . N.p., 2001. Web. 19 Nov. 2013. <http://www2.edc.org/mathproblems/problems/printProblems/nsPigeonHole.pdf>.