Puzzler!

[HandsandDreams]

Has anyone ever heard of the proof that one equals two?

X = Y

2X = YX  [Multiply both sides by X]

2X - Y^2 = YX - Y^2  [Subtract Y^2 from both sides]

(X-Y)(X+Y) = 2(X-Y)  [Factor; remember FOIL?]

X+Y = Y  [Divide both sides by (X-Y)]

1+1 = 1  [Assign value 1 to X and Y, since X = Y]

2 = 1

I promise you there's a flaw.  Can you spot it?  Took me a year.

[AlP]

X = Y
2X = YX  Multiply both sides by X

[spoiler:1ekse37i]Didn't you just multiply the left side by 2 and the right side by X? It should be

X = Y
X^2 = YX

Also, why does X = Y? I would agree with X = X or Y = Y.[/spoiler:1ekse37i]

[AlP]

I slightly modified this puzzle to make it harder to search for! Haha!

A woman will be elected as US President in the future.

This is a claim and has truth value. It is either true or false.

If the original claim is true:
Then it is true today that a woman will be elected as US President in the future.
Since it is true today, it is necessary that a woman will be elected in the future.

If the original claim is false:
Then it is false today that a woman will be elected as US President in the future.
Since it is false today, it is necessary that a woman will not be elected.

Therefore, whether a woman will be elected as US President in the future is predetermined because it is already true or false.

[HandsandDreams]

Oh crap, you're right, sorry!  I made a mistake in step 4 also.

The real puzzle should read:

X = Y [Because we said so; X and Y have the same value]

X^2 = YX [Multiply both sides by X]

X^2 - Y^2 = YX - Y^2 [Subtract Y^2 from both sides]

(X+Y)(X-Y) = Y(X-Y) [Factor; remember FOIL?]

X+Y = Y [Divide both sides by (X-Y)]

1+1 = 1 [Assign value 1 to X and Y, since X = Y]

2 = 1

[AlP]

[spoiler:2n2sq3p9]Well then X-Y is potentially zero when you divide. You can't divide by zero. And as it turns that if X = 1 and Y = 1 then its a divide by zero. Is that it?[/spoiler:2n2sq3p9]

[karadan]

Squares A and B are exactly the same shade of grey.

This one does my head in. Not a puzzle, but certainly puzzling.

[HandsandDreams]

[spoiler:1khdf23l]Well then X-Y is potentially zero when you divide. You can't divide by zero. And as it turns that if X = 1 and Y = 1 then its a divide by zero. Is that it?[/spoiler:1khdf23l]

You got it!

[bowmore]

Has anyone ever heard of the proof that one equals two?

X = Y
...
X+Y = Y  [Divide both sides by (X-Y)]

[spoiler:3dwo6y24]if X=Y then X-Y = 0, you can't divide by zero.[/spoiler:3dwo6y24]

[Whitney]

This one does my head in. Not a puzzle, but certainly puzzling.

I hate those...I even checked to make sure they were the same...and they were.  It has to do with the way colors that are next to the color affect how it is perceived.

[karadan]

This one does my head in. Not a puzzle, but certainly puzzling.

I hate those...I even checked to make sure they were the same...and they were.  It has to do with the way colors that are next to the color affect how it is perceived.

Totally. I still can't look at it and see them as both the same shade of grey. I think it is impossible. Someone in my office wouldn't believe it, so i had to do a demo with MS paint.  

[thenolan]

Spoiler alert!!!









How many triangles? How many line segments? How do you know?









I began by assuming three triangles in each figure, and calculated the areas using the formula 1/2*base*height. The small triangles don't add up to the same area as the large "triangles". Then I cheated and looked up why: basic trigonometry, i.e. compare the tangent ratios of the apparently equal angles. The larger figures are two different quadrilaterals whose area differs by exactly one square unit. The top figure's area is 1/2 square unit less that the imaginary larger triangle, and the bottom figure's area is 1/2 square unit larger than the imaginary larger triangle.

[NaturaLCalamity]

Squares A and B are exactly the same shade of grey.

This one does my head in. Not a puzzle, but certainly puzzling.

Huh? I don't really get this illusion. They are clearly different shades...how can they be the same?

[karadan]

Huh? I don't really get this illusion. They are clearly different shades...how can they be the same?

Use a paint tool to move one of the squares over the other. you'll see that they are indeed the same shade of grey!

[JillSwift]

Huh? I don't really get this illusion. They are clearly different shades...how can they be the same?

Perception. You have a brain that evolved to detect stuff in the shadows (among other detection tricks), so it's "adjusting" perceived luminescence of the squares that appear in a shadow.

[karadan]

What Jill said