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

Let’s prove that: $2 = 1$

Here’s the proof:

Let’s start by establishing some variables: $a = 1$ $b = 1$

Okay, so if that’s true, then we know: $a = b$

In algebra, we learned we could multiply both sides of the equation, so: $a \times a = b \times a$

or $a^2 = b a$

And of course, we can also subtract a number from both sides of the equation: $a^2 - b^2 = ba - b^2$

Now, we can factor that equation to get: $(a + b)(a - b) = b(a - b)$

Of course, $(a - b)$ cancels out, so: $(a + b) = b$

Putting back in the numbers, we see that: $(1 + 1) = 1$

or $2 = 1$

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”

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!