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[youtube]http://youtube.com/watch?v=_bFJrZb8LFw[/youtube]

Will someone kindly explain this one to me? I apparently lack the intellectual horsepower.

Very clever. The "extra" square is being taken from along the diagonal cut line.

Look at the height of the lower square in the row of 4 that on the left at :25.

Then look at the height of the square which is going to is going to be slide into that space.

Thanks TAM. You made my brain hurt for a hot second....

Steve, you've got better eyes than I do. I'm still not seeing it.

OOOOOOwwwwwwwwwww! My head.

I don't see it either. Kinda like this guy.

http://www.youtube.com/watch?v=ZTy3qG_qInU&feature=kp" onclick="window.open(this.href);return false;

steveincowtown wrote:Very clever. The "extra" square is being taken from along the diagonal cut line.

Look at the height of the lower square in the row of 4 that on the left at :25.

Then look at the height of the square which is going to is going to be slide into that space.

Thanks TAM. You made my brain hurt for a hot second....

Yep! The blocks are not the same size. The reconstructed rectangle is not quite as tall as the original. I haven't quite worked out the math behind it, nor probably will, but the reconstructed rectangle is short off the top by the area of the removed block.

The answer stands out like a sore thumb if you perform the trick ever so slightly different:

If you slide the single piece up out of the way first, then slide the three squares off to the side. THEN slide the top section down and to the left, then the three around to the other side your brain locks on to whats happening better.

Or think of it like this: The whole set is actually 1/4 of a rectangle piece shorter.

One of those should get your head around it.

The volume comes out of the third row from the bottom. This is why they left a gap when they put it back together otherwise it would be obvious that this row was significantly shorter than the other rows.

Here is a pic of the square missing with the cut line pushed together and placed back into the paper it was cut from. Notice the gap at the top and the shorter row.

If your cuts and lines were accurate all your rows would be the same length and the volume of the gap at the top would be exactly the volume of one rectangle.

By jove, I think you've discovered the perpetual chocolate bar. My wife will be thrilled.

SQURIELL!!!