This is a classic brain teaser I learned in middle school (or “junior high school” where I grew up).

Let’s prove that:

Here’s the proof:

Let’s start by establishing some variables:

Okay, so if that’s true, then we know:

In algebra, we learned we could multiply both sides of the equation, so:

or

And of course, we can also subtract a number from both sides of the equation:

Now, we can factor that equation to get:

Of course, cancels out, so:

Putting back in the numbers, we see that:

or

And there is our proof!

To misquote Groucho Marx:

“An eighth grader could understand that! Someone fetch me an eighth grader!”

2 Responses to “Brain Teaser: Proof That 2 = 1”

When I was a math teacher, I gave my students the following little ditty:

In your attempt to prove your theorem

And show you are the hero

Be careful how you do your math

And don’t divide by zero.

🙂

Nice!