Math for dummies part 1

I was recently in the elevator, and there were two others besides myself in there. There were two floor buttons pressed. For the time being, assume that we are going up and there are only two floors remaining. I smiled as I quickly deduced that at least two of us would get off at the same floor.

I am starting this series because there are some extremely simple mathematical concepts that are actually quite profound. These are some of the fundamental theorems of math, but they can be understood by any 7 year old. It is a shame that 7 year olds don't get taught this stuff. It's simply bril.

Pigeon Hole theorem:

"If there are N pigeons and N-1 pigeonholes, then there must be at least one pigeonhole with more than one pigeon."

Proof:

Imagine, you have a certain amount of pigeons on your roof. You raise them for companionship, for transporting important missives via courier pigeon, and (of course), for food. Now, you have, let's say, 4 pigeons. Alas, you only have 3 pigeon holes. Not realising the impact of the this mathematical model and needing to house your pigeons in pigeonholes, you stuff one pigeon in hole 1.

You now have three pigeons and two empty pigeonholes. You cannot put another pigeon in pigeonhole 1 unless you want to end this proof prematurely. Besides, you have empty holes to use. So you stuff a pigeon in hole 2.

Now you have two pigeons and one emtpy pigeonhole. So you stuff a pigeon in hole 3.

Now you have one pigeon and no empty pigeonholes. This last pigeon must become a roommate to an existing pigeon filling an existing pigeonhole.

Easy.