May have been posted before:

a = x
a+a = a+x
2a = a+x
2a-2x = a+x-2x
2(a-x) = a+x-2x
2(a-x) = a-x
2 = 1


???

wrong forum.....wait, wrong website!

Flowers2 said:

So what's your answer then?

It's too late at night for me to sit and figure out formulas.

I probably wouldn't bother anyway

obsessed said:

I'm with you, it's late lol .. to get the energy to try to do formulas @ 1:25am will exhaust me more lol .. but I do love this..

it could be any number you want.


Wait....2=1???
[Edited 12/13/08 22:42pm]

ArielB said:

I saw that and decided to figure this out tomorrow.. this requires energy I don't have right now..

I don't even understand one word.

abierman said:

Yeah, like one with smart people.

~throws stone~

Since a=x, a-x=0
So in the last term, where you divide the left and right part by a-x, you're divinding by zero, which is not possible.

What'd I win?

AlfofMelmak said:

Doofus Of The Week Award!

But seriously, I wish I had a brain like that.

Good one, Favourite Left Leg.

Ahem, Urban dictionary:


Perfect recipe for hairy legs

AlfofMelmak said:

I don't see any dividing done. Only multiplying.

I don't really understand how this is a brain teaser. It's just wrong.

If a = x, then a-x=0

so 2(a-x) = a-x
is 2(0) = 0

the last step made in the original post was dividing (a-x)/(a-x) and taking that to be one, but 0/0 is 0, of course. I'm sure Moonbeam or another math geek can provide a better technical explanation with proper terminology, but I'm pretty certain that's all there is to it in laymen's terms.
[Edited 12/14/08 9:26am]

damosuzuki said:

There's no dividing in the original post, just multiplying.

I think the point of this math problem is that "a" could equal 2 and "x" could equal 1 (or vice versa) and all the equations would work out. But that doesn't mean that 2 equals 1.

Efan said:

There's an 'implied' division in the last two steps to reduce the equation.

To get from:
2(a-x) = a-x

To
2 = 1

You have to take this step:

[2(a-x)]/(a-x) = (a-x)/(a-x)

Which if a >< x, would then prove that 2=1. But a=x, so both sides of the equation = 0.

I may be wrong, but that's all I see there.
[Edited 12/14/08 9:53am]

Efan said:

And how about that last step, what happens there?
2(a-x)=a-x
2=1

The left term is divided by (a-x), to end up with 2. To keep equality between the left and right term, the latter also must be divided by (a-x), which indeed would be 1.
But since a-x=0, you would be dividing by zero.

too much for my dumb brain

AlfofMelmak said:

I could be totally looking at this wrong, but I didn't think these were steps; I thought they were individual equations. So the first one after a = x (a+a = a+x) is separate and doesn't have anything to do with the last one or any of the other ones. I thought that the point was just showing that you could do all of those equations using either 1 or 2. But you would have to have both a and x equal 1 or both a and x equal 2; you can't have them equal the two numbers at the same time. So it doesn't really seem like a brain teaser; just an oddity of how you can use both numbers to fit into these equations. Does that make sense? I could be totally off on what this is talking about...

Efan said:

These are a series of steps, of equations.

This is where the equation gets "zeroed" out:
2a-2x = a+x-2x

At this point, they've made the equation state 0 = 0, and it carries through until the last step, where they "lie" to you by stating that 0/0=1, not 0.

damosuzuki said:

If I had a gif of Emily Littella saying, "Oh, that's different. Never mind!" I would post it here. I misunderstood, so disregard what I was saying.

Efan said:

Every line is exactly the same as the next; You can rewrite every equation as long as you do the same to the left as the right part of the equation.
so to: a = x
is added an a to both sides of the =
-> a+a = a+x, then rewrite to 2a = a+x

now substract 2x both left and right.
2a-2x = a+x-2x

rewrites to
2(a-x) = a+x-2x
2(a-x) = a-x

so this equation is exactly the same as a=x
And it doesn't matter which number a or x is, it's the same. It has nothing to do with them being 1 or 2.
if x = 0, so is a: fill in the last equation: 2(0) = 0
if x = 1, so is a: fill in the last equation: 2(0) = 0
if x = 11224868632433432.93278482764832648, so is a: fill in the last equation: 2(0) = 0

The teaser is in the last 2 lines; going from 2(a-x) to just 2, you would have to divide by (a-x). If the first line would have read a-x=0, you would have immediately seen the solution, but instead it was shown as a=x

AlfofMelmak said:

Co-sign.

mcmeekle said:

zero point zero

im lost