Figure this one out--Perpetual Puzzle

[LennG]

https://www.youtube.com/watch?v=lICA96wxiuI

[Bob In PA]

If you can't figure it out, I'll bet your "whiz" daughter can explain it.  Bob

[LennG]

If you can't figure it out, I'll bet your "whiz" daughter can explain it.  Bob

Can you?

[Bob In PA]

Can you?

Yes, I believe so.  Let me know when to give hint (if ever).  Bob

[LennG]

Yes, I believe so.  Let me know when to give hint (if ever).  Bob

For me, anytime is good enough. My daughter is busy.

[Bob In PA]

Watch and consider EVERYTHING the magician does, and ask yourself why.  There is one final thing he does NOT do at the end.  Ask yourself why not, and you'll be able to explain most of it. 

First hint: this is an extremely clever magic trick (NOT trick photography, and definitely NOT the "reality" it appears to represent).  There is no true sleight-of-hand, like switching the pieces for some of a different shape.

Kudos to whoever thought of converting it into a trick.  I've seen those same 5 pieces presented as a puzzle (instructions: assemble into a rectangle) after which they add the 6th piece, and give the same instructions.

As a kid I was for a short period of time an amateur magician (strong emphasis on the word "amateur" LOL) so I am somewhat aware of certain possibilities that you may not have considered.

I'll throw out a more substantial hint tomorrow if no one figures it out by then.  It's clever, deceptive, and the magician got away with it right before your very eyes.  (This is a weak attempt to be "mysterious" LOL).

Bob

[ozzie]

I love magic and have a few books on the subject, but I can't figure this one out.
It is fun to watch and be amazed though!!

[Bob In PA]

I love magic and have a few books on the subject, but I can't figure this one out.
It is fun to watch and be amazed though!!

oz: True. For many people, revealing the secret spoils the fun. An axiom of magic is "a good magician never reveals the secret." I figure it's ok for me to do so because, like I implied, I was not a "good" magician.  LOL

[Blue4Life]

I am not a "magician" by any means, but had been pretty good at math, algebra, etc.

The area of the rectangle changed with the additional pieces, but not its general shape. Note, that the ratio between the long and short side of the rectangle changed as well.With that change, the frame size's side ratio had to change as well to accommodate the rearranged shape of the rectangle.

The trick is a somewhat "flexible" frame, that extends/contracts, based on the number shapes in the rectangle. Designing this magician toy had probably been the hard part. Detecting the "trick" in this puzzle should not "puzzle" mathematicians for long. Pun intended...

[Bob In PA]

B4F: Yes indeed. It is a trick frame.  What gives it away is that the BOX disappears from the picture after the frame is removed.

Otherwise, the audience might expect the magician to put the frame back in the box after the trick ends (which would be impossible).  So you may ask... why have a box at all?  I believe I know the answer.

We can only speculate about the mechanism, but my guess is that the frame is "spring-loaded" internally (with a stretchy cover over the exterior) so merely removing it from the box allows it to expand automatically.

The amount of expansion to permit addition of the sixth piece is imperceptible (because the sixth piece represents a minuscule percentage of the entire surface area of the other five pieces).

If you watch carefully you can see the magician give the frame a slight "tug" as he removes it from the box.

NOW.... how and when does the magician expand the frame to the second "level" which permits addition of the seventh and final piece?

I have no idea.  I guess the mechanism has a "notch" to make it stop expanding at the first expansion level, and maybe pushing gently inward on opposite ends of the frame slightly will trigger the final expansion.

Bob

[Ed Vette]

The first rectangle was never put in the frame because it was too small. The third rectangle was too big but if you notice he only showed one side of the frame. He put the frame on the third rectangle on an angle because I suspect the bottom of the top side of the frame is carved out and a portion of the frame fits over a portion of the third rectangle.

[Bob In PA]

The first rectangle was never put in the frame because it was too small. The third rectangle was too big but if you notice he only showed one side of the frame. He put the frame on the third rectangle on an angle because I suspect the bottom of the top side of the frame is carved out and a portion of the frame fits over a portion of the third rectangle.

Ed: Shrewd, and possible, but I like my idea better. LOL  Also, the other person whose hands we see was permitted to touch the frame, and unless that's just an example of "false advertising" the implication is that the audience might be permitted to examine the frame, in which case they would see that the shape of the frame was not entirely "square" on all sides. My guess (concerning the spring mechanism) would be that it locks in place after the final expansion and will not collapse, so it can be presented to the audience for examination. The magician would have a small key to insert in a tiny hole in order to release the lock and permit the frame to collapse so it would fit back into the box for storage (at which point the trick would be "reset"). There is a small area visible on the frame that appears to have a tiny black mark or hole in it, which would confirm my suspicion. Bob

[Jolly Blue Giant]

Man that got a laugh out of me. I was blown away until I read through all the posts. Good one! 

[DaveBrown74]

This reminded me a little bit of the "infinite chocolate bar" trick. See below:

https://www.youtube.com/watch?v=z7tRr49qZfo

[Bob In PA]

The chocolate bar video is important to our discussion of the Perpetual Puzzle. It illustrates how small a percentage the sixth tile (small square) is compared to the surface area of the entire puzzle.

It also shows why there's a good chance Ed's approach (which has the elegance of simplicity) could be correct.  The dimensions of the entire puzzle change very little upon addition of the sixth and seventh pieces.

In the chocolate bar puzzle the slight "mismatch" between the two diagonal pieces at the conclusion of the trick is actually equal to the surface area of the piece that has been excluded upon re-assembly of the bar.

Bob