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.

    🙂