Ok ladies and gentlemen... some of you know those puzzles, but I guess some of you do not.

Here are some excellent examples which do not need much comments, as the pictures speak
for themselves. So... let the puzzle-music start:

















Those were made by some exceptional puzzlers and artists. For more, search the net.
Or, if you find such a puzzle which you believe is BRILLIANT, please share it with us!




Pantazis

Here's a video of one of these puzzles, but this one is fairly easy to work out.

Alex

Planet Perplex has several of these:
http://www.planetperplex.com/en/sliding_puzzles.html

Livewire has a free version at:
http://www.puzzles.ca/magical_envelope_puzzle.html

The vanishing Ninja:
http://www.dojopress.com/tvn.html

You can buy several version at Archimedes' Lab:
http://www.cafepress.com/mariejo2/345778

They call them "geometric erodings" or "stereophanic puzzles"
http://www.archimedes-lab.org/page5b.html#
http://www.archimedes-lab.org/page7b.html

You can print one:
http://www.archimedes-lab.org/workshopvanishbird.html
http://www.archimedes-lab.org/Gallery/new_optical_illusions/pages/101-Magic_eggs_VAN.html

There is an explanation of the Vanishing Leprechaun at this site:
http://britton.disted.camosun.bc.ca/jblep1.htm
It was designed by Ms. Pat (Patterson) Lyons circa 1968 and is related to the DeLand Paradox.

Other geometrical paradoxes are illustrated here:
http://library.thinkquest.org/28049/geometrical_vanishes.htm

Here is a video of one classic geometric fallacy:
http://www.youtube.com/watch?v=sDerqFGmwNI

"Who Turned to Doggie Doo?" by Robin Debreuil is nice entertaining example of a vanish.
You can see it on John Rausch's site here:
http://www.puzzleworld.org/PuzzleWorld/puz/who_turned_to_doggie_doo.htm

and at Debreuil's site:
http://debreuil.com/ddw/puzjava/picmove.htm
where you can download a free printable version.

The Magic Egg is another classic - see it here (requires Shockwave plugin):
http://www.psychologie.tu-dresden.de/i1/kaw/diverses%20Material/www.illusionworks.com/html/vanishing_egg.html
The actual antique postcard can sometimes be found on eBay.

That site also has an explanation of how these puzzles work.
It also mentions a criminal use of the vanish:
" The principle is very old and probably originated as a early method for counterfeiting money. William Hooper in his book Rational Recreations, published in 1794, described the paradox as "Geometric Money," It is possible to cut 9 bills into eighteen parts (following the pattern of the lines) and then to rearrange them to make ten bills. To foil this method, the two numbers on all U.S. currency is placed on opposite ends, one high and one low. In this way, counterfeit bills using this method are easy to detect since their numbers will not match correctly. In fact, in 1968, a man in London was sentenced to eight years in prison for using this scheme on British five-pound notes."

I think it is interesting how Pat Lyons came out with the Leprechauns in 1968! Coincidence?

Two informative articles are a section in Martin Gardner's Mathematics, Magic and Mystery (1958) and an article by Mel Stover in the November 1980 issue of Games magazine.
Also discussed in Gardner's "Wheels, Life, and Other Mathematical Amusements" in chapter 12.
Martin Gardner calls it "the principle of concealed distribution."

Try Mel Stover's Pencils here:
http://www.puzzles.com/puzzleplayground/StoversPencils/StoversPencils.htm

Check out a version by Mark Setteducati here:
http://www.marksetteducati.com/apeardisapear.htm

See a great trick by Masao Atsukawa called Warp 9:
http://www.youtube.com/watch?v=nvUpFC49oFM

Winston Freer's Tile Puzzle:
http://www.youtube.com/watch?v=_LY7mf49l5k

a similar effect:
http://www.youtube.com/watch?v=uMIm2Md4uIA
You can find that trick sold on eBay

Another video:
http://www.youtube.com/watch?v=slHo07SQz54

A fun version at the dharmainitiative:
http://www.dharmainitiative.it/index.php?id=test&n=8

That site also provides info on the history of the vanish:
"The first example of vanishing area puzzles was reported in the book Libro d'Architettura Primo by Sebastiano Serlio (1475-1554)"
"The first description and mathematical explanation of the vanish paradox was found in a math puzzle book with a very long title: Rational Recreations: In which the Principles of Numbers and Natural Philosophy are Clearly and Copiously Elucidated, by a Series of Easy, Entertaining, Interesting Experiments. Among which are All Those Commonly Performed with the Cards, L. Davis; J. Robson; B. Law; and G. Robinson, 1774 by William Hooper. Probably Hooper cribbed the puzzle from the book Nouvelles récréations physiques et mathématiques by the French author Edmé Gilles Guyot (1770)"

And gives links to download the book from google:
http://books.google.it/books?id=mGxbAAAAQAAJ&dq=william%20hooper%20Rational%20Recreations&pg=PA286#v=onepage&q&f=false

You can buy copies of Sam Loyd's vanish puzzles, and try them online, here:
http://www.samuelloyd.com/
http://www.samloyd.com/vanishing-puzzles/index.html

The Jerry Slocum collection at the Lilly Library contains a few:
http://webapp1.dlib.indiana.edu/slocum/results/result.do?display=thumbcap&action=browse&page=1&pagesize=20&query=collection%3Alilly%2Fslocum+classification:8*

I have a copy of the vintage French boxed puzzle "L'Echiquier Fantastique"

Yes!!! More mind-blowing links! Thanks Rob!!!! (the videos were done by some excellent performers!)




Pantazis

I have a few of these in my collection. Very nice puzzles and the mathematical principle behind them is very interesting

Missing Square

The Magic Square

The Impossible Square

Here's one similar to Sam Loyd's "Get Off the Earth" puzzle
which I found in my collection. It is called... Bushwacky!






Pantazis

I love these kinds of puzzles, but they drive me crazy. Especially the ones with shapes.