# Introduction to Pigeonhole Principle

## Homework Statement

Give a sample problem its solution employing Pigeonhole Principle

## Homework Equations

Pigeonhole Principle

## The Attempt at a Solution

We have this homework about pigeonhole principle which hasn't been discussed yet, but we need to present an example and present it in class,, I've been searching, I get the holes and pigeons like logic stuff,, If i were to get an example i would use the birthday problem which is easy,, but i dont know if this is relevant,, if there's anyone who could explain or could give any easy example.. this would really help.. also please provide with explanation and solution tnx

Try to do this one:

Say I choose 51 numbers from 1,2,...,100. Then there will be at least 2 numbers who do not have a common prime factor.

so pigeons would be the 100 and 51 would be the pigeon box right? or 2?
so how do i equate it? do i use subset?

No, the pigeon boxes are somewhat more complicated.

Hint: the numbers k and k+1 do not have common prime divisor.