Via Mark Frauenfelder, I came across a variation of a popular trick that is particularly well done.
For those seeking to figure it out, here are screen caps of the three situations.
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Those who know how it is done can say so in the comments.
Mano Singham
Just another Freethought Blogs site
I think the trick is the rectangle gets a little taller with each piece, but it’s by such a small amount that it can still “fit” in the frame, just most snugly. The real trick would be to build it in the frame instead of adding the frame after.
You can actually see the large gap at the top of the frame in the middle image, the height of which would appear to be the difference in the length of the long sides of piece 4.
My guess is that the frame is spring-loaded in the vertical direction. Note that the pieces fit snugly in the frame when the frame is in the cardboard box… I wonder what the initial configuration looks like with the frame out of the box?
Aha! I was right -- at 0:33 when the box is lifted clear after taking out the pieces, the top rail clearly slides as it is gripped with the right thumb.
Yea.. I think its a combination of what was said above: the frame does expand vertically after the first configuration. 2nd configuration fits the larger frame but with some extra space. 3rd configuration fits the same larger frame snuggly.
My guess on the engineering of the frame is that the top bar of the frame starts off a bit lower, looking like this: ㅂ. The two tops of the side bars are hidden in the packaging.
Something very like this was shown on QI a couple of years ago. If I remember the secret is that the angles on the sides of the pieces are not quite true -- the apparent right angles are not true right angles, but the shift is so slight our brains rationalise them into squares. So there’s plenty of give in the shape and room for additional area if you shuffle them round.
cartomancer,
I think that the puzzle you are referring to is this one below that I wrote about back in 2008. (You need to scroll down to the Post Script and click on the link.) I give the solution in the comments.
Or to rephrase it: Human perception is really bad at accounting for long, thin spaces that actually have the same area as one (or more, in the case of the OP) square(ish) space.
If you measure the left edge of piece 3, it is larger than the left edge of piece 1. Hence the final rectangle is taller by just the amount needed to accommodate the additional area of pieces 6 and 7.
Banach Tarski!