Can you explain this puzzle?

  WhiteTruckMan 23:21 31 Dec 2006
Locked

click here

My brother emailed it to me and its destroying my brain cell by cell. Every time I look at it now, poof! there go a few more cells. I flatly refuse to print it out, cut it out and play with the pieces. Can anyone else explain this just by looking at it, because its got me stumped!

WTM

  Brumas 23:29 31 Dec 2006

Thanks for that mate, just what I needed - something to irritate my every waking minute!!!
;o)

  Forum Editor 23:40 31 Dec 2006

that when you rearrange a series of shapes they must always cover the same area. Geometry doesn't work that way. The same area is enclosed, but some of it isn't covered.

Don't agonise over it - it'll be next year in twenty minutes or so, and it will be last year's frustration.

  Blackhat 23:58 31 Dec 2006

OK FE solve this before 2008.

We start with two quantities a & b which are equal.

Equation 1. a=b

We can multiply both sides of an equation by the same value without affecting the equality. Lets multiply both sides by a.

Equation 2. a²=axb

We can subtract the same value from both sides of an equation by the same value without affecting the equality. So lets subtract b² from both sides.

Equation 3. a²-b²=axb-b²

a²-b² can also be represented by (a+b)x(a-b).

axb-b² Is also the product of bx(a-b). so we now have,

Equation 4. (a+b)x(a-b)= bx(a-b)

We can divide both sides of an equation by the same value without affecting the equality. Lets divide by (a-b). This means the (a-b) factor drops from both sides. We are left with,

Equation 5. a+b=b

Since a=b we can say that a+b is the same as b+b therefore;

Equation 6. b+b=b

  WhiteTruckMan 00:15 01 Jan 2007

If a=b

then a-b=0, so

(a+b)x0=0,

so really its just a long winded way of saying 0=0

but if I follow FE's comments about geometry then I should be able to add 50 square feet to my house just by rearranging the internal partition walls.

WTM

  p;3 00:16 01 Jan 2007

if you can link it other than by imageshack I'll have a look; I am afraid I now refuse to click on anything that uses imageshack facilities

  Blackhat 00:25 01 Jan 2007

WhiteTruckMan.

Thanks for that, I thought I might have FE pondering for a while, it took me along time to work it out and some of my friends still don't know the answer.
Happy new year.

  hzhzhzhz 00:25 01 Jan 2007
  Blackhat 00:32 01 Jan 2007

Why are there so many smart people out there, can't we just have a bit of fun with puzzles before we get the answers? Thats what puzzles are about, trying to work someting out yourself can be fun and a useful distraction.

  Forum Editor 01:28 01 Jan 2007

Only if a couple of your rooms are right-angled triangles.

  WhiteTruckMan 01:41 01 Jan 2007

well he practiced a bit before hand on my place.

But seriously that description really does apply to the early 19th century building where we rent our shop. I swear there isnt a right angle in the place. I dont know about a listed building, but it certainly is listing a bit...

But to go back to my original puzzle, it never occurred to me that I was looking at an optical illusion. If i HAD cut the blinkin' thing out I would have sussed it. Ah well, live and learn.

I think I will leave this thread for a little while and if no-one has any other comments just quietly tick it later.

WTM

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