Introduction to Pigeonhole Principle

[saintrenz]

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 don't 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

 

[micromass]

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.

 

[saintrenz]

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?

 

[micromass]

No, the pigeon boxes are somewhat more complicated.

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